M. Dolores Jiménez Gamero

Universidad de Sevilla | US · Statistics and Operations Research

Arriaza et al (Metrika 82:99–124, 2019) introduced the right and left shape functions, which enjoy interesting properties in terms of describing the global form of a distribution. This paper proposes and studies nonparametric estimators of those functions. The estimators involve nonparametric estimation of the quantile and density functions. Pointw...

This paper uses independence-type characterizations to propose a class of test statistics which can be used for testing goodness-of-fit with several classes of null distributions. The resulting tests are consistent against fixed alternatives. Some limiting and small sample properties of the test statistics are explored. In comparison with common un...

This paper studies the problem of simultaneously testing that each of k independent samples come from a normal population. The means and variances of those populations may differ. The proposed procedures are based on the BHEP test and they allow k to increase, which can be even larger than the sample sizes.

Equivalence tests have received increasing attention in the last years, especially in experimental applied fields such as Biology, Medicine or Pharmacology. In the statistical applications in these fields, the multinomial distribution is perhaps one of the discrete distributions most widely used. The family of \(\phi \)-divergence measures have sup...

A general and relatively simple method for construction of multivariate goodness–of–fit tests is introduced. The proposed test is applied to elliptical distributions. The method is based on a characterization of probability distributions via their characteristic function. The consistency and other limit properties of the new test statistics are stu...

A general and relatively simple method for construction of multivariate goodness-of-fit tests is introduced. The proposed test is applied to elliptical distributions. The method is based on a characterization of probability distributions via their characteristic function. The consistency and other limit properties of the new test statistics are stu...

The usefulness of the parameters (e.g., slope, aspect) derived from a Digital Elevation Model (DEM) is limited by its accuracy. In this paper, a thematic-like quality control (class-based) of aspect and slope classes is proposed. A product can be compared against a reference dataset, which provides the quality requirements to be achieved, by compar...

Given k independent samples of functional data, this paper deals with the problem of testing for the equality of their mean functions. In contrast to the classical setting, where k is kept fixed and the sample size from each population increases without bound, here k is assumed to be large and the size of each sample is either bounded or small in c...

Since the seminal paper by Bates and Granger in 1969, a vast number of ensemble methods that combine different base regressors to generate a unique one have been proposed in the literature. The so-obtained regressor method may have better accuracy than its components, but at the same time it may overfit, it may be distorted by base regressors with...

Given k independent samples with finite but arbitrary dimension, this paper deals with the problem of testing for the equality of their distributions that can be continuous, discrete or mixed. In contrast to the classical setting where k is assumed to be fixed and the sample size from each population increases without bound, here k is assumed to be...

The geometric distribution is one of the most widely used count distributions. Novel goodness of fit tests for this distribution are suggested taking advantage of a characterization of that distribution in terms of a differential equation involving its probability generating function. Several ways of looking at the characterization allow us to deri...

A common assumption in non-parametric regression models is the independence of the covariate and the error. Some procedures have been suggested for testing that hypothesis. This paper considers a test, whose test statistic compares estimators of the joint and the product of the marginal characteristic functions of the covariate and the error. It is...

A test approach to the model selection problem for multinomial data based on penalized ϕ-divergences is proposed. The test statistic is a sample version of the difference of the distances between the population and each competing model. The null distribution of the test statistic is derived, showing that it depends on whether the competing models i...

This paper proposes and studies a novel test for the geometric distribution which is based on a characterization of that law in terms of the conditional expectation of the second order statistic, given the value of the first order statistic. The asymptotic null distribution of the test statistic and its limit under general conditions are derived, p...

This paper proposes and studies two new classes of tests for exponentiality. Both of them are based on Basu's characterization of the exponential distribution. The null distributions of the test statistics are parameter free. Moreover, conveniently normalized, they are asymptotically normally distributed. The large sample behaviour of the proposed...

Since the seminal paper by Bates and Granger in 1969, a vast number of ensemble methods that combine different base regressors to generate a unique one have been proposed in the literature. The so-obtained regressor method may have better accuracy than its components , but at the same time it may overfit, it may be distorted by base regressors with...

Let X1,X2,… be independent and identically distributed random elements taking values in a separable Hilbert space ℍ. With applications for functional data in mind, ℍ may be regarded as a space of square‐integrable functions, defined on a compact interval. We propose and study a novel test of the hypothesis H0 that X1 has some unspecified non‐degene...

We propose a class of goodness-of-fit test procedures for arbitrary parametric families of circular distributions with unknown parameters. The tests make use of the specific form of the characteristic function of the family being tested, and are shown to be consistent. We derive the asymptotic null distribution and suggest that the new method be im...

COVID-19 is an infectious disease that was first identified in China in December 2019. Subsequently COVID-19 started to spread broadly, to also arrive in Spain by the end of Jan-uary 2020. This pandemic triggered confinement measures, in order to reduce the expansion of the virus so as not to saturate the health care system. With the aim of providi...

The one-parameter Bell family of distributions, introduced by Castellares et al. (Appl Math Model 56:172–185, 2018), is useful for modeling count data. This paper proposes and studies a goodness-of-fit test for this distribution, which is consistent against fixed alternatives. The finite sample performance of the proposed test is investigated by me...

A recent method for estimating a lower bound of the population size in capture-recapture samples is studied. Specifically, some asymptotic properties, such as strong consistency and asymptotic normality, are provided. The introduced estimator is based on the empirical probability generating function (pgf) of the observed data, and it is consistent...

Let $X_1,X_2, \ldots$ be independent and identically distributed random elements taking values in a separable Hilbert space $\mathbb{H}$. With applications for functional data in mind, $\mathbb{H}$ may be regarded as a space of square-integrable functions, defined on a compact interval. We propose and study a novel test of the hypothesis $H_0$ that...

We consider a goodness-of-fit test for certain parametrizations of conditionally heteroscedastic time series with unobserved components. Our test is quite general in that it can be employed to validate any given specification of arbitrary order and may even be invoked for testing not just GARCH models but also some related models such as autoregres...

A test for the equality of error distributions in two nonparametric regression models is proposed. The test statistic is based on comparing the empirical characteristic functions of the residuals calculated from independent samples of the models. The asymptotic null distribution of the test statistic cannot be used to estimate its null distribution...

This article deals with the algebra of gH-differentiable interval-valued functions. Specifically, we give conditions for the gH-differentiability of the sum and the gH-difference of two gH-differentiable interval-valued functions; we also consider the product and the composition of a differentiable real function and a gH-differentiable interval-val...

In practice, count data exhibit over-dispersion, zero-inflation and even heavy tails. The Poisson–Tweedie distribution is a flexible parametric family able to accommodate these features. This paper proposes and studies a computationally convenient goodness-of-fit test for this distribution, which is based on an empirical counterpart of a system of...

The problem of testing for the parametric form of the conditional variance is considered in a fully nonparametric regression model. A test statistic based on a weighted L2-distance between the empirical characteristic functions of residuals constructed under the null hypothesis and under the alternative is proposed and studied theoretically. The nu...

The problem of testing for the parametric form of the conditional variance is considered in a fully nonparametric regression model. A test statistic based on a weighted $L_2$-distance between the empirical characteristic functions of residuals constructed under the null hypothesis and under the alternative is proposed and studied theoretically. The...

This paper focuses on the consequences of assuming a wrong model for multinomial data when using minimum penalized ϕ -divergence, also known as minimum penalized disparity estimators, to estimate the model parameters. These estimators are shown to converge to a well-defined limit. An application of the results obtained shows that a parametric boots...

A class of tests for testing independence whose test statistic is an L2-norm of the difference between the joint empirical characteristic function and the product of the marginal empirical characteristic functions associated with a sample is considered. Since the null distribution of these test statistics is unknown, some approximations are investi...

Auxiliary information \({\varvec{x}}\) is commonly used in survey sampling at the estimation stage. We propose an estimator of the finite population distribution function \(F_{y}(t)\) when \({\varvec{x}}\) is available for all units in the population and related to the study variable y by a superpopulation model. The new estimator integrates ideas...

Several procedures have been proposed for testing goodness-of-fit to the error distribution in nonparametric regression models. The null distribution of the associated test statistics is usually approximated by means of a parametric bootstrap which, under certain conditions, provides a consistent estimator. This paper considers a goodness-of-fit te...

In De Campos Ibáñez and González-Muñoz (Fuzzy Sets Syst 29:145–154, 1989, [6]), Goestschel and Voxman (Fuzzy Sets Syst 18:31–43, 1986, [7]) the authors considered a linear ordering on the space of fuzzy intervals. For each fuzzy mapping (fuzzy interval-valued mapping) F, based on the aforementioned linear ordering, they introduced a real-valued fun...

We generalize a recent class of tests for univariate normality that are based on the empirical moment generating function to the multivariate setting, thus obtaining a class of affine invariant, consistent and easy-to-use goodness-of-fit tests for multinormality. The test statistics are suitably weighted $L^2$-statistics, and we provide their asymp...

Several procedures have been proposed for testing the equality of error distributions in two or more nonparametric regression models. Here we deal with methods based on comparing estimators of the cumulative distribution function (CDF) of the errors in each population to an estimator of the common CDF under the null hypothesis. The null distributio...

This paper studies properties of parameter estimators obtained by minimizing a distance between the empirical probability generating function and the probability generating function of a model for count data. Specifically, it is shown that, under certain not restrictive conditions, the resulting estimators are consistent and, suitably normalized, a...

We provide novel characterizations of multivariate normality that incorporate both the characteristic function and the moment generating function, and we employ these results to construct a class of affine invariant, consistent and easy-to-use goodness-of-fit tests for normality. The test statistics are suitably weighted $L^2$-statistics, and we pr...

Goodness-of-fit tests for the innovation distribution in GARCH models based on measuring deviations between the empirical characteristic function of the residuals and the characteristic function under the null hypothesis have been proposed in the literature. The asymptotic distributions of these test statistics depend on unknown quantities, so thei...

Muth introduced a probability distribution with application in reliability theory. We propose a new model from the Muth law. This paper studies its statistical properties, such as the computation of the moments, computer generation of pseudo-random data and the behavior of the failure rate function, among others. The estimation of parameters is car...

This paper studies the estimation of the characteristic function of a finite population. Specifically, the weak convergence of the finite population empirical characteristic process is studied. Under suitable assumptions, it has the same limit as the empirical characteristic process for independent, identically distributed data from a random variab...

Tests are proposed for the assumption that the conditional distribution of a multivariate GARCH process is elliptic. These tests are of Kolmogorov–Smirnov and Cramér–von Mises–type and make use of the common geometry underlying the characteristic function of any spherically symmetric distribution. The asymptotic null distribution of the test statis...

A class of tests for the two-sample problem for count data whose test statistic is an -norm of the difference between the empirical probability generating functions associated with each sample is considered. The tests can be applied to count data of any arbitrary fixed dimension. Since the null distribution of the test statistic is unknown, some ap...

A class of tests for the two-sample problem whose test statistic is an norm of the difference of the empirical characteristic functions of the samples is considered. The null distribution can be estimated by means of bootstrap or permutation procedures. Although very easy to implement, such procedures can become computationally expensive as the sam...

The Log–Lindley distribution is a continuous probability model with useful applications in insurance and inventory management. In this note, it is proven that pseudo-random data from this model can be generated by computer via the Lambert function. It is proposed a reparametrization suitable to get estimates of the parameters. Moreover, it is showe...

The problem of estimation of the shape parameter in a generalized half-logistic distribution for progressively type-II censored samples is of interest in reliability and survival analysis. In this paper, Bayesian methods of estimation based on quadratic and Linex loss functions are proposed. Closed expressions and approximations are obtained for th...

The evaluation of the spatial similarity of two observed point patterns is an important issue in spatial data quality assessment. In this work we propose a formal procedure that takes advantage of the joint use of space-filling curves and the multinomial model in order to establish a statistical test to compare spatial point patterns. In this mix,...

Bivariate count data arise in several different disciplines and the bivariate Poisson distribution is commonly used to model them. This paper proposes and studies a computationally convenient goodness-of-fit test for this distribution, which is based on an empirical counterpart of a system of equations. The test is consistent against fixed alternat...

In this paper, two new maximum likelihood methods are proposed to estimate the unknown sample size in a simple random sample from an absolutely continuous population. These methods are based on the number of records and the record values in the sample. The use of these methods is explored through simulations. An application to a real data set is al...

This article deals with generalized differentiable fuzzy functions. Specifically, we give some characterizations of generalized Hukuhara differentiable fuzzy functions through the differentiability of their endpoint functions. Then, we introduce a differentiability concept that is more general than the generalized Hukuhara differentiability and ext...

In this paper we are interested in checking whether the conditional variances are equal in k ≥ 2 location-scale regression models. Our procedure is fully nonparametric and is based on the comparison of the error distributions under the null hypothesis of equality of variances and without making use of this null hypothesis. We propose four test stat...

The penalized calibration technique in survey sampling combines usual calibration and soft calibration by introducing a penalty term. Certain relevant estimates in survey sampling can be considered as penalized calibration estimates obtained as particular cases from an optimization problem with a common basic structure. In this framework, a case de...

The Muth distribution is a continuous random variable introduced in the context of reliability theory. In this paper, some mathematical properties of the model are derived, including analytical expressions for the moment generating function, moments, mode, quantile function and moments of the order statistics. In this regard, the generalized integr...

A class of goodness-of-fit tests whose test statistic is an norm of the difference of the empirical characteristic function of the sample and a parametric estimate of the characteristic function in the null hypothesis, is considered. The null distribution is usually estimated through a parametric bootstrap. Although very easy to implement, the para...

Many models of asymmetric distributions proposed in the statistical literature are obtained by transforming an arbitrary symmetric distribution by means of a skewing mechanism. In certain important cases, the resultant skewed distribution shares some properties of its symmetric antecedent. Because of this inheritance, it would be interesting to tes...

Bivariate and multivariate exponential distributions are widely applied in several areas such as reliability, queueing systems or hydrology. A frequently used bivariate exponential distribution is the Moran-Downton distribution. Because of this reason, this paper proposes a goodness-of-fit test for this distribution. The test statistic exploits the...

A class of goodness-of-fit tests of the Cramér–von Mises type is considered. More specifically, the test statistic of each test is an -norm of the difference between the empirical characteristic function associated with a random sample and a parametric estimator of the characteristic function of the population in the null hypothesis. The null distr...

A test approach to the model selection problem based on characteristic functions (CFs) is proposed. The scheme is close to that proposed by Vuong (Econometrica 57:257–306, 1989), which is based on comparing estimates of the Kullback–Leibler distance between each candidate model and the true population. Other discrepancy measures could be used. This...

A class of goodness-of-fit tests is considered. The test statistic of each test in this class is an L2-norm of the difference between the empirical characteristic function associated with a random sample and an estimator of the characteristic function of the population in the null hypothesis. Because it is not always possible to give an easily comp...

This article studies a new procedure to test for the equality of k regression curves in a fully non-parametric context. The test is based on the comparison of empirical estimators of the characteristic functions of the regression residuals in each population. The asymptotic behaviour of the test statistic is studied in detail. It is shown that unde...

The class of generalized autoregressive conditional heteroscedastic (GARCH) models has been proved to be particularly valuable in modeling financial data. This paper is devoted to study the empirical characteristic function process of the residuals. Specifically, it is shown that such process uniformly converges to the population characteristic fun...

Two families of tests for testing uniform association in cross-classification having ordered categories are considered. The test statistics of the tests in these two families are based on Burbea–Rao divergences between certain functions of the observed data. The objective of this paper is to compare these families. The comparison is done both theor...

There is an increasing number of goodness-of-fit tests whose test statistics measure deviations between the empirical characteristic function and an estimated characteristic function of the distribution in the null hypothesis. With the aim of overcoming certain computational difficulties with the calculation of some of these test statistics, a tran...

The problem of testing uniform association in cross-classifications having ordered categories is considered. Two families of test statistics, both based on divergences between certain functions of the observed data, are studied and compared. Our theoretical study is based on asymptotic properties. For each family, two consistent approximations to t...

We provide an explicit analytical solution for a logarithmic integral in terms of the Lerch transcendent function together with the generalized Stirling numbers of the first kind. For some special cases of interest in statistical applications, the explicit solution can be expressed in terms of the polylogarithm function together with the aforementi...

The properties of minimum φ-divergence estimators for parametric multinomial populations are well-known when the assumed parametric model is true, namely, they are consistent and asymptotically normally distributed. Here we study these properties when the parametric model is not assumed to be correctly specified. Under certain conditions, these est...

This paper studies goodness-of-fit tests for the bivariate Poisson distribution. Specifically, we propose and study several Cramér–von Mises type tests based on the empirical probability generating function. They are consistent against fixed alternatives for adequate choices of the weight function involved in their definition. They are also able to...

This paper is devoted to studying differential calculus for interval-valued functions by using the generalized Hukuhara differentiability, which is the most general concept of differentiability for interval-valued functions. Conditions, examples and counterexamples for limit, continuity, integrability and differentiability are given. Special emphas...

Based on the use of calibration techniques as a way of handling nonresponse, case-deletion diagnostics for calibration estimators are proposed. A deleted case is dealt with as it were a nonresponse case. Two types of diagnostics are proposed: one compares the calibration weights and the other compares the estimates. These diagnostics are studied in...

We propose approximations to the moments, different possibilities for the limiting distributions and approximate confidence intervals for the maximum-likelihood estimator of a given parametric function when sampling from partially non-regular log-exponential models. Our results are applicable to the two-parameter exponential, power-function and Par...

The skew t distribution is a flexible parametric family to fit data, because it includes parameters that let us regulate skewness and kurtosis. A problem with this distribution is that, for moderate sample sizes, the maximum likelihood estimator of the shape parameter is infinite with positive probability. In order to try to solve this problem, Sar...

The consequences of model misspecification for multinomial data when using minimum [phi]-divergence or minimum disparity estimators to estimate the model parameters are considered. These estimators are shown to converge to a well-defined limit. Two applications of the results obtained are considered. First, it is proved that the bootstrap consisten...

We consider the problem of testing uniform association in cross-classifications with ordered categories taking as test statistic a Rϕ divergence. The asymptotic null distribution of any test statistic in this class is not free because it depends on the unknown true vector of probabilities, so in practice one has to approximate it in order to get an...

In this paper we study the generalized derivative and the π-derivative for interval-valued functions. We show the connections between these derivatives. Some illustrative examples and applications to interval differential equations and fuzzy functions are presented.

Four strategies for bias correction of the maximum likelihood estimator of the parameters in the Type I generalized logistic distribution are studied. First, we consider an analytic bias-corrected estimator, which is obtained by deriving an analytic expression for the bias to order n ; second, a method based on modifying the likelihood equations; t...

This study concerns autonomous ground vehicles performing missions of observation or surveillance. These missions are accomplished under the supervision of human operators, who can also remotely control the unmanned vehicle. This kind of human-machine ...

Due to the fact that the spatial outlier observations depend on the neighborhood where they are located, a definition of δ-outlier is given, δ being the diameter of the neighborhood. Two methods to identify δ-outliers are proposed. One of them for continuous random fields and the other for Gaussian continuous random fields.

In this paper, we consider the problem of testing uniform association in cross-classifications having ordered categories, taking as test statistic one in the family proposed by Conde and Salicrú [J. Conde, M. Salicrú, Uniform association in contingency tables associated to Csiszár divergence, Statistics and Probability Letters 37 (1998) 149–154]. W...

A widely used distribution to model mixed data is the conditional Gaussian model. We study the problem of testing the homogeneity of two conditional Gaussian populations. With this aim, we consider as test statistic a sample version of the Kullback-Leibler distance between these populations. It is shown that the test that rejects the null hypothesi...

A class of goodness-of-fit tests based on the empirical characteristic function is studied. They can be applied to continuous as well as to discrete or mixed data with any arbitrary fixed dimension. The tests are consistent against any fixed alternative for suitable choices of the weight function involved in the definition of the test statistic. Th...

We consider the problem of testing the equality of ν (ν≥2) multinomial populations, taking as test statistic a sample version of an f-dissimilarity between the populations, obtained by the replacement of the unknown parameters in the expression of the f-dissimilarity among the theoretical populations, by their maximum likelihood estimators. The nul...

In this paper, a test for the homogeneity of two bidimensional populations is proposed. It is based on the L 2-norm of the difference between the empirical characteristic functions associated with independent random samples from each population. We first approximate this norm and then we give two bootstrap algorithms to consistently estimate the nu...

Since bootstrap samples are simple random samples with replacement from the original sample, the information content of some bootstrap samples can be very low. To avoid this fact, several variants of the classical bootstrap have been proposed. In this paper, we consider two of them: the sequential or Poisson bootstrap and the reduced bootstrap. Bot...

The π-derivative for fuzzy function is considered. Con- sequently, using this π-derivative we study fuzzy differentuial equa- tions. In particular, we build a solution for a fuzzy differential equa- tion with the help of a system of ordinary differential equations which is generates of the π-derivative. Keywords— π-derivative for set valued functio...

This article presents a proposal for the decomposition of large ranges of uncertainty associated with the Cartesian product of two fuzzy intervals. We compute an approximation of the fuzzy set obtained by applying extension principle to a real function by means of this decomposition and piecewise linearization of the function. It is proved the effi...

A class of tests for the two sample problem that is based on the empirical characteristic function is investigated. They can be applied to continuous as well as to discrete data of any arbitrary fixed dimension. The tests are consistent against any fixed alternatives for adequate choices of the weight function involved in the definition of the test...

Bagging is based on the combination of models fitted to bootstrap samples of a training data set. There is considerable evidence that such ensemble method can significantly reduce the variance of the prediction model. However, several techniques have been proposed to achieve a variance reduction in the proper bootstrap resampling process, as in our...

We give an algorithm to decompose a fuzzy interval u. Using this decomposition and the multilinearization of a univariate function f, we obtain an approximation of the fuzzy interval fˆ(u), where fˆ is obtained from f by applying the extension principle. We provide approximation bounds. Some numeric illustration is provided.

In this paper we consider the reduced bootstrap, that consists of only considering those bootstrap samples satisfying k1[less-than-or-equals, slant][nu]n[less-than-or-equals, slant]k2, for some 1[less-than-or-equals, slant]k1[less-than-or-equals, slant]k2[less-than-or-equals, slant]n, where [nu]n is the number of distinct original observations in t...

In this paper, to test goodness of fit to any fixed distribution of errors in multivariate linear models, we consider a weighted integral of the squared modulus of the difference between the empirical characteristic function of the residuals and the characteristic function under the null hypothesis. We study the limiting behaviour of this test stat...

In this paper we show that the bootstrap approximates consistently the distribution of the sample Matusita distance between two conditional Gaussian distributions, under the null hypothesis of homogeneity. We also study by simulation the finite sample performance of the bootstrap distribution and compare it with the asymptotic approximation.

We introduce the concept of fuzzy quasilinear space and fuzzy quasilinear operator. Moreover we state some properties and give results which extend to the fuzzy context some results of linear functional analysis.

Summary Since it is not always possible to calculate bootstrap estimators, they are usually approximated by simulation. In this article, we propose a bootstrap bias estimator for smooth functions of sample means that has less mean squared error, due to the simulation process, than the ordinary bootstrap. The estimator is based on shrinking the boot...

One of the areas of Statistics in which the influence analysis has been widely studied is the multiple linear regression model. Nevertheless, the influence diagnostics proposed in this context cannot be applied to regression in complex survey, under randomized inference, since the i.i.d. case does not incorporate any probability weighting or popula...

Bagging is an ensemble method proposed to improve the predictive performance of learning algorithms, being specially effective when applied to unstable predictors. It is based on the aggregation of a certain number of prediction models, each one generated from a bootstrap sample of the available training set. We introduce an alternative method for...