
Leandro PardoComplutense University of Madrid | UCM · Departamento de Estadística e Investigación Operativa
Leandro Pardo
Mathematics, Statistics PhD
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331
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Introduction
Publications
Publications (331)
In this paper, we introduce a novel family of estimators for the shape and scale parameters of the log-logistic distribution being robust when rank set sample method for data selection is used. Rank set sampling effectively reduces the influence of extreme data points. The log-logistic distribution is a versatile model, suitable in various fields s...
Penalized logistic regression is extremely useful for binary classification with large number of covariates (higher than the sample size), having several real life applications, including genomic disease classification. However, the existing methods based on the likelihood loss function are sensitive to data contamination and other noise and, hence...
Canonical Correlation Analysis (CCA) infers a pairwise linear relationship between two groups of random variables, X and Y. In this paper, we present a new procedure based on Rényi’s pseudodistances (RP) aiming to detect linear and non-linear relationships between the two groups. RP canonical analysis (RPCCA) finds canonical coefficient vectors, a...
Inferential methods under extreme form of censoring are of interest in reliability theory because of their applicability to practical engineering problems. interval-censored data naturally appear in many situations wherein the exact failure times cannot be observed, but we can only know if the product has failed before a certain inspection time or...
Model selection criteria are rules used to select the best statistical model among a set of candidate models, striking a trade-off between goodness of fit and model complexity. Most popular model selection criteria measure the goodness of fit trough the model log-likelihood function, yielding to non-robust criteria. This paper presents a new family...
In this paper, we introduce the restricted minimum density power divergence Gaussian estimator (MDPDGE) and study its main asymptotic properties. In addition, we examine it robustness through its influence function analysis. Restricted estimators are required in many practical situations, such as testing composite null hypotheses, and we provide in...
One‐shot devices analysis involves an extreme case of interval censoring, wherein one can only know whether the failure time is either before or after the test time. Some kind of one‐shot devices do not get destroyed when tested, and so can continue within the experiment, providing extra information for inference, if they did not fail before an ins...
Zhang (2019) presented a general estimation approach based on the Gaussian distribution for general parametric models where the likelihood of the data is difficult to obtain or unknown, but the mean and variance-covariance matrix are known. Castilla and Zografos (2021) extended the method to density power divergence-based estimators, which are more...
One-shot devices analysis involves an extreme case of interval censoring, wherein one can only know whether the failure time is before the test time. Some kind of one-shot units do not get destroyed when tested, and then survival units can continue within the test providing extra information for inference. This not-destructiveness is a great advant...
Since the two seminal papers by Fisher (Biometrika 10:507–521, 1915; Metron 1:1–32, 1921) were published, the test under a fixed value correlation coefficient null hypothesis for the bivariate normal distribution constitutes an important statistical problem. In the framework of asymptotic robust statistics, it remains being a topic of great interes...
Coronavirus disease 2019 (COVID19) has triggered a global pandemic affecting millions of people. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) causing the COVID-19 disease is hypothesized to gain entry into humans via the airway epithelium, where it initiates a host response. The expression levels of genes at the upper airway that in...
Most work on one-shot devices assume that there is only one possible cause of device failure. However, in practice, it is often the case that the products under study can experience any one of various possible causes of failure. Robust estimators and Wald-type tests are developed here for the case of one-shot devices under competing risks. An exten...
One-shot devices are product or equipment that can be used only once, so they get destroyed when tested. However, the destructiveness assumption may not be necessary in many practical applications such as assessing the effect of temperature on some electronic components, yielding to the so called non-destructive one-shot devices. Further, one-shot...
In real life we often deal with independent but not identically distributed observations (i.n.i.d.o), for which the most well-known statistical model is the multiple linear regression model (MLRM) with non-random covariates. While the classical methods are based on the maximum likelihood estimator (MLE), it is well known its lack of robustness to s...
One-shot devices data represent an extreme case of interval censoring.Some kind of one-shot units do not get destroyed when tested, and so, survival units can continue within the test providing extra information about their lifetime. Moreover, one-shot devices may last for long times under normal operating conditions, and so accelerated life tests...
The Rao's score, Wald and likelihood ratio tests are the most common procedures for testing hypotheses in parametric models. None of the three test statistics is uniformly superior to the other two in relation with the power function, and moreover, they are first-order equivalent and asymptotically optimal. Conversely, these three classical tests p...
One-shot devices analysis involves an extreme case of interval censoring, wherein one can only know whether the failure time is either before or after the test time. Some kind of one-shot devices do not get destroyed when tested, and so can continue within the experiment, providing extra information for inference, if they did not fail before an ins...
Since the two seminal papers by Fisher (1915, 1921) were published, the test under a fixed value correlation coefficient null hypothesis for the bivariate normal distribution constitutes an important statistical problem. In the framework of asymptotic robust statistics, it remains being a topic of great interest to be investigated. For this and oth...
Minimum Renyi’s pseudodistance estimators (MRPEs) enjoy good robustness properties without a significant loss of efficiency in general statistical models, and, in particular, for linear regression models (LRMs). In this line, Castilla et al. considered robust Wald-type test statistics in LRMs based on these MRPEs. In this paper, we extend the theor...
In this paper we apply divergence measures to empirical likelihood applied to logistic regression models. We define a family of empirical test statistics based on divergence measures, called empirical phi-divergence test statistics, extending the empirical likelihood ratio test. We study the asymptotic distribution of these empirical test statistic...
Hypothesis testing is one of the fundamental paradigms of statistical inference. The three canonical hypothesis testing procedures available in the statistical literature are the likelihood ratio (LR) test, the Wald test and the Rao (score) test. All of them have good optimality properties and past research has not identified any of these three pro...
Penalized logistic regression is extremely useful for binary classification with a large number of covariates (significantly higher than the sample size), having several real life applications, including genomic disease classification. However, the existing methods based on the likelihood based loss function are sensitive to data contamination and...
The approach for estimating and testing based on divergence measures has become, in the last 30 years, a very popular technique not only in the field of statistics, but also in other areas, such as machine learning, pattern recognition, etc [...]
This paper is aimed to present a robust extension of the classical Rao test statistic, in the context of composite likelihood ideas and methods. The Rao-type test statistics are defined on the basis of the composite minimum power divergence estimators instead of the composite maximum likelihood estimator. These Rao-type test statistics are used to...
In this paper we propose a new family of estimators, Minimum Density Power Divergence Estimators (MDPDE), as a robust generalization of maximum likelihood estimators (MLE) for the loglinear model with multinomial sampling by using the Density Power Divergence (DPD) measure introduced by Basu et al. (1998). Based on these estimators, we further deve...
In this article, we develop robust estimators and tests for one-shot device testing under proportional hazards assumption based on divergence measures. Through a detailed Monte–Carlo simulation study and a numerical example, the developed inferential procedures are shown to be more robust against data contamination than the classical procedures, ba...
In real life we often deal with independent but not identically distributed observations (i.n.i.d.o), for which the most well-known statistical model is the multiple linear regression model (MLRM) without random covariates. While the classical methods are based on the maximum likelihood estimator (MLE), it is well known its lack of robustness to sm...
This paper presents new families of Rao-type test statistics based on the minimum density power divergence estimators which provide robust generalizations for testing simple and composite null hypotheses. The asymptotic null distributions of the proposed tests are obtained and their robustness properties are also theoretically studied. Numerical il...
In this chapter, we provide a detailed review of divergence-based robust inferential methods for one-shot device testing under different lifetime distributions. Proposed estimators and Wald-type tests are shown to possess a more robust behavior than the classical maximum likelihood estimator (MLE) and Wald test. Some simulation results and real dat...
Analyzing polytomous response from a complex survey scheme, like stratified or cluster sampling is very crucial in several socio-economics applications. We present a class of minimum quasi weighted density power divergence estimators for the polytomous logistic regression model with such a complex survey. This family of semiparametric estimators is...
The semi-parametric Cox proportional hazards regression model has been widely used for many years in several applied sciences. However, a fully parametric proportional hazards model, if appropriately assumed, can often lead to more efficient inference. To tackle the extreme non-robustness of the traditional maximum likelihood estimator in the prese...
Several regularization methods have been considered over the last decade for sparse high-dimensional linear regression models, but the most common ones use the least square (quadratic) or likelihood loss and hence are not robust against data contamination. Some authors have overcome the problem of non-robustness by considering suitable loss functio...
We introduce a new family of Wald-type tests, based on minimum Rényi pseudodistance estimators, for testing general linear hypotheses and the variance of the residuals in the multiple regression model. The classical Wald test, based on the maximum likelihood estimator, can be seen as a particular case inside our family. Theoretical results, support...
Maji et al. [Robust statistical inference based on the C-divergence family. Ann Inst Stat Math. 2019;71:1289–1322] introduced the minimum C-divergence estimators and plugging them in the C-divergence measures give test statistics for testing simple null and composite null hypotheses. One inconvenience of these test statistics is that their asymptot...
Introduced robust density‐based estimators in the context of one‐shot devices with exponential lifetimes under a single stress factor. However, it is usual to have several stress factors in industrial experiments involving one‐shot devices. In this paper, the weighted minimum density power divergence estimators (WMDPDEs) are developed as a natural...
In this paper, we develop robust estimators and tests for one-shot device testing under proportional hazards assumption based on divergence measures. Through a detailed Monte Carlo simulation study and a numerical example, the developed inferential procedures are shown to be more robust than the classical procedures, based on maximum likelihood est...
Most work on one-shot devices assume that there is only one possible cause of device failure. However, in practice, it is often the case that the products under study can experience any one of various possible causes of failure. Robust estimators and Wald-type tests are developed here for the case of one-shot devices under competing risks. An exten...
We consider the problem of simultaneous model selection and the estimation of regression coefficients in high-dimensional linear regression models of non-polynomial order, an extremely important problem of the recent era. The adaptive penalty functions are used in this regard to achieve the oracle model selection property along with easier computat...
In this paper a family of Wald-type test statistics for linear hypotheses in the logistic regression model with complex sample survey data is introduced and its properties are explored. The family of tests considered is based on the pseudo minimum phi-divergence estimator that contains, as a particular case, the pseudo maximum likelihood estimator....
This paper presents a model selection criterion in a composite likelihood framework based on density power divergence measures and in the composite minimum density power divergence estimators, which depends on an tuning parameter α . After introducing such a criterion, some asymptotic properties are established. We present a simulation study and tw...
Traditionally, the Dirichlet-multinomial distribution has been recognized as a key model for contingency tables generated by cluster sampling schemes. There are, however, other possible distributions appropriate for these contingency tables. This paper introduces new statistics capable of testing log-linear modeling hypotheses with distributional u...
Classical inferential methods for one-shot device testing data from an accelerated life-test are based on maximum likelihood estimators (MLEs) of model parameters. However, the lack of robustness of MLE is well-known. In this article, we develop robust estimators for one-shot device testing by assuming a Weibull distribution as a lifetime model. Wa...
It is well-known that in some situations it is not easy to compute the likelihood function as the datasets might be large or the model is too complex. In that contexts composite likelihood, derived by multiplying the likelihoods of subjects of the variables, may be useful. The extension of the classical likelihood ratio test statistics to the frame...
Due to its flexibility, gamma distribution is commonly used for lifetime data analysis in reliability and survival studies, and especially in one-shot device testing data. In the study of such data, inducing more failures by accelerated life tests is a common practice, to obtain more lifetime information within a relatively short period of time. In...
This paper presents new families of Rao-type test statistics based on the minimum density power divergence estimators which provide robust generalizations for testing simple and composite null hypotheses. The asymptotic null distributions of the proposed tests are obtained and their robustness properties are also theoretically studied. Numerical il...
In the last decades the interest in statistical methods based on information measures and particularly in pseudodistances or divergences has grown substantially [...]
Analyzing polytomous response from a complex survey scheme, like stratified or cluster sampling is very crucial in several socio-economics applications. We present a class of minimum quasi weighted density power divergence estimators for the polytomous logistic regression model with such a complex survey. This family of semiparametric estimators is...
The log-normal distribution is one of the most common distributions used for modeling skewed and positive data. It frequently arises in many disciplines of science, specially in the biological and medical sciences. The statistical analysis for comparing the means of two independent log-normal distributions is an issue of significant interest. In th...
Imposing restrictions without assuming underlying distributions to modelize complex realities is a valuable methodological tool. However, if a subset of restrictions were not correctly specified, the usual test-statistics for correctly specified models tend to reject erronously a simple null hypothesis. In this setting, we may say that the model su...
This paper describes a family of divergences, named herein as the C-divergence family, which is a generalized version of the power divergence family and also includes the density power divergence family as a particular member of this class. We explore the connection of this family with other divergence families and establish several characteristics...
This paper considers the problem of robust hypothesis testing under non-identically distributed data. We propose Wald-type tests for both simple and composite hypothesis for independent but non-homogeneous observations based on the robust minimum density power divergence estimator of the common underlying parameter. Asymptotic and theoretical robus...
The log-normal distribution is one of the most common distributions used for modeling skewed and positive data. It frequently arises in many disciplines of science, specially in the biological and medical sciences. The statistical analysis for comparing the means of two independent log-normal distributions is an issue of significant interest. In th...
We consider the problem of robust inference under the important generalized linear model (GLM) with stochastic covariates. We derive the properties of the minimum density power divergence estimator of the parameters in GLM with random design and used this estimator to propose a robust Wald-type test for testing any general composite null hypothesis...
We consider the problem of robust inference under the generalized linear model (GLM) with stochastic covariates. We derive the properties of the minimum density power divergence estimator of the parameters in GLM with random design and use this estimator to propose robust Wald-type tests for testing any general composite null hypothesis about the G...
This paper develops a new family of estimators, MDPDEs, as a robust generalization of maximum likelihood estimator for the polytomous logistic regression model (PLRM) by using the DPD measure. Based on these estimators, the family of Wald-type test statistics for linear hypotheses is introduced and their robust properties are theoretically studied...
A new family of minimum distance estimators for binary logistic regression models based on ϕ -divergence measures is introduced. The so called “pseudo minimum phi-divergence estimator”(PM ϕ E) family is presented as an extension of “minimum phi-divergence estimator” (M ϕ E) for general sample survey designs and contains, as a particular case, the p...
In this paper, a robust version of theWald test statistic for composite likelihood is considered by using the composite minimum density power divergence estimator instead of the composite maximum likelihood estimator. This new family of test statistics will be called Wald-type test statistics. The problem of testing a simple and a composite null hy...
In any parametric inference problem, the robustness of the procedure is a real concern. A procedure which retains a high degree of efficiency under the model and simultaneously provides stable inference under data contamination is preferable in any practical situation over another procedure which achieves its efficiency at the cost of robustness or...
In this paper a robust version of the Wald test statistic for composite likelihood is considered by using the composite minimum density power divergence estimator instead of the composite maximum likelihood estimator. This new family of test statistics will be called Wald-type test statistics. The problem of testing a simple and a composite null hy...
Technical Report - Bayesian and Interdisciplinary Research Unit, Indian Statistical Institute, 2013:
The power divergence (PD) and the density power divergence (DPD) families have proved to be useful tools in the area of robust inference. The families have striking similarities, but also have fundamental differences; yet both families are extremel...
Randomly censored survival data are frequently encountered in applied sciences including biomedical and reliability applications. We propose Wald-type tests for testing parametric statistical hypothesis, both simple as well as composite, for randomly censored data using the M-estimators under a fully parametric set-up. We propose a consistent estim...
Randomly censored survival data are frequently encountered in applied sciences including biomedical or reliability applications and clinical trial analyses. Testing the significance of statistical hypotheses is crucial in such analyses to get conclusive inference but the existing likelihood based tests, under a fully parametric model, are extremely...
This paper considers the problem of robust hypothesis testing under non-identically distributed data. We propose Wald-type tests for both simple and composite hypothesis for independent but non-homogeneous observations based on the robust minimum density power divergence estimator of the common underlying parameter. Asymptotic and theoretical robus...
In this paper we explore the possibilities of applying \(\phi \)-divergence measures in inferential problems in the field of latent class models (LCMs) for multinomial data. We first treat the problem of estimating the model parameters. As explained below, minimum \(\phi \)-divergence estimators (M\(\phi \)Es) considered in this paper are a natural...
In this paper a new robust estimator, modified median estimator, is introduced and studied for the logistic regression model. This estimator is based on the median estimator considered in Hobza et al. [Robust median estimator in logistic regression. J Stat Plan Inference. 2008;138:3822–3840]. Its asymptotic distribution is obtained. Using the modif...
In this paper a robust version of the classical Wald test statistics for linear hypothesis in the logistic regression model is introduced and its properties are explored. We study the problem under the assumption of random covariates although some ideas with non random covariates are also considered. The family of tests considered is based on the m...
This paper develops a new family of estimators, the minimum density power divergence estimators (MDPDEs), for the parameters of the one-shot device model as well as a new family of test statistics, Z-type test statistics based on MDPDEs, for testing the corresponding model parameters. The family of MDPDEs contains as a particular case the maximum l...
Parametric hypothesis testing associated with two independent samples arises frequently in several applications in biology, medical sciences, epidemiology, reliability and many more. In this paper, we propose robust Wald-type tests for testing such two sample problems using the minimum density power divergence estimators of the underlying parameter...
Parametric hypothesis testing associated with two independent samples arises frequently in several applications in biology, medical sciences, epidemiology, reliability and many more. In this paper, we propose robust Wald-type tests for testing such two sample problems using the minimum density power divergence estimators of the underlying parameter...
It is usual to rely on the quasi-likelihood methods for deriving statistical
methods applied to clustered multinomial data with no underlying distribution.
Even though extensive literature can be encountered for these kind of data
sets, there are few investigations to deal with unequal cluster sizes. This
paper aims to contribute to fill this gap b...
A new family of minimum distance estimators for binary logistic regression models based on $\phi$-divergence measures is introduced. The so called "pseudo minimum phi-divergence estimator"(PM$\phi$E) family is presented as an extension of "minimum phi-divergence estimator" (M$\phi$E) for general sample survey designs and contains, as a particular c...
Traditionally, the Dirichlet-multinomial distribution has been recognized as a key model for contingency tables generated by cluster sampling schemes. There are, however, other possible distributions appropriate for these contingency tables. This paper introduces new test-statistics capable to test log-linear modeling hypotheses with no distributio...
In this paper a robust version of the classical Wald test statistics for linear hypothesis in the logistic regression model is introduced and its properties are explored. We study the problem under the assumption of random covariates although some ideas with non random covariates are also considered. The family of tests considered is based on the m...
This article develops the theoretical framework needed to study the multinomial logistic regression model for complex sample design with pseudo minimum phi-divergence estimators. Through a numerical example and simulation study new estimators are proposed for the parameter of the logistic regression model with overdispersed multinomial distribution...
This article develops the theoretical framework needed to study the multinomial logistic regression model for complex sample design with pseudo minimum phi-divergence estimators. Through a numerical example and simulation study new estimators are proposed for the parameter of the logistic regression model with overdispersed multinomial distribution...
It is well-known that in some situations it is not easy to compute the likelihood function as the datasets might be large or the model is too complex. In that contexts composite likelihood, derived by multiplying the likelihoods of subjects of the variables, may be useful. The extension of the classical likelihood ratio test statistics to the frame...
We consider a robust version of the classical Wald test statistics for testing simple and composite null hypotheses for general parametric models. These test statistics are based on the minimum density power divergence estimators instead of the maximum likelihood estimators. An extensive study of their robustness properties is given though the infl...
Empirical phi-divergence test-statistics have demostrated to be a useful
technique for the simple null hypothesis to improve the finite sample behaviour
of the classical likelihood ratio test-statistic, as well asfor model
misspecification problems, in both cases for the one population problem. This
paper introduces this methodology for two sample...