Natalie Neumeyer

University of Hamburg | UHH · Department of Mathematics

In transformation regression models, the response is transformed before fitting a regression model to covariates and transformed response. We assume such a model where the errors are independent from the covariates and the regression function is modeled nonparametrically. We suggest a test for goodness-of-fit of a parametric transformation class ba...

This paper deals with an estimation of the dependence structure of a multidimensional response variable in the presence of a multivariate covariate. It is assumed that the covariate affects only the marginal distributions through regression models while the dependence structure, which is described by a copula, is unaffected. A parametric estimation...

We consider a nonparametric heteroscedastic time series regression model and suggest testing procedures to detect changes in the conditional variance function. The tests are based on a sequential marked empirical process and thus combine classical CUSUM tests from change point analyis with marked empirical process approaches known from goodness‐of‐...

Semiparametric transformation models are considered, where after pre-estimation of a parametric transformation of the response the data are modeled by means of nonparametric regression. Subsequent procedures for testing lack-of-fit of the regression function and for significance of covariates are suggested. In contrast to existing procedures, the t...

In transformation regression models the response is transformed before fitting a regression model to covariates and transformed response. We assume such a model where the errors are independent from the covariates and the regression function is modeled nonparametrically. We suggest a test for goodness-of-fit of a parametric transformation class bas...

We consider a nonparametric heteroscedastic time series regression model and suggest testing procedures to detect changes in the conditional variance function. The tests are based on a sequential marked empirical process and thus combine classical CUSUM tests with marked empirical process approaches known from goodness-of-fit testing. The tests are...

This paper deals with a situation when one is interested in the dependence structure of a multidimensional response variable in the presence of a multivariate covariate. It is assumed that the covariate affects only the marginal distributions through regression models while the dependence structure, which is described by a copula, is unaffected. A...

A weakly dependent time series regression model with multivariate covariates and univariate observations is considered, for which we develop a procedure to detect whether the nonparametric conditional mean function is stable in time against change point alternatives. Our proposal is based on a modified CUSUM type test procedure, which uses a sequen...

In the context of nonparametric regression models with one-sided errors, we consider parametric transformations of the response variable in order to obtain independence between the errors and the covariates. In view of estimating the tranformation parameter , we use a minimum distance approach and show the uniform consistency of the estimator under...

In the context of nonparametric regression models with one-sided errors, we consider parametric transformations of the response variable in order to obtain independence between the errors and the covariates. We focus in this paper on stritcly increasing and continuous transformations. In view of estimating the tranformation parameter, we use a mini...

In this paper we consider a location model of the form $Y = m(X) + \varepsilon$, where $m(\cdot)$ is the unknown regression function, the error $\varepsilon$ is independent of the $p$-dimensional covariate $X$ and $E(\varepsilon)=0$. Given i.i.d. data $(X_1,Y_1),\ldots,(X_n,Y_n)$ and given an estimator $\hat m(\cdot)$ of the function $m(\cdot)$ (wh...

We consider semiparametric transformation models, where after pre-estimation of a parametric transformation of the response the data are modeled by means of nonparametric regression. We suggest subsequent procedures for testing lack-of-fit of the regression function and for significance of covariables, which -- in contrast to procedures from the li...

This paper is concerned with modeling the dependence structure of two (or more) time-series in the presence of a (possible multivariate) covariate which may include past values of the time series. We assume that the covariate influences only the conditional mean and the conditional variance of each of the time series but the distribution of the sta...

In this paper an autoregressive time series model with conditional heteroscedasticity is considered, where both conditional mean and conditional variance function are modeled nonparametrically. A test for the model assumption of independence of innovations from past time series values is suggested. The test is based on an weighted $L^2$-distance of...

In this paper the nonparametric quantile regression model is considered in a location-scale context. The asymptotic properties of the empirical independence process based on covariates and estimated residuals are investigated. In particular an asymptotic expansion and weak convergence to a Gaussian process are proved. The results can, on the one ha...

This paper is concerned with testing rationality restrictions using quantile regression methods. Specifically, we consider negative semidefiniteness of the Slutsky matrix, arguably the core restriction implied by utility maximization. We consider a heterogeneous population characterized by a system of nonseparable structural equations with infinite...

In this paper we consider a heteroscedastic transformation model, where the transformation belongs to a parametric family of monotone transformations, the regression and variance function are modelled nonparametrically and the error is independent of the multidimensional covariates. In this model, we first consider the estimation of the unknown com...

We consider a nonparametric regression model with one-sided errors and regression function in a general H\"older class. Our aim is inference on the error distribution. To this end we estimate the regression function via minimization of the local integral of a polynomial approximation. We show uniform rates of convergence for the simple regression e...

In this article, we propose a new test for additivity in nonparametric quantile regression with a high-dimensional predictor. Asymptotic normality of the corresponding test statistic (after appropriate standardization) is established under the null hypothesis, local and fixed alternatives. We also propose a bootstrap procedure which can be used to...

We propose several new tests for monotonicity of regression functions based on different empirical processes of residuals. The residuals are obtained from recently developed simple kernel based estimators for increasing regression functions based on increasing rearrangements of unconstrained nonparametric estimators. The test statistics are estimat...

We suggest a new consistent asymptotically distribution-free test for independence of the components of bivariate random variables. The approach combines methods of order-selection tests with nonparametric copula density estimation. We deduce the asymptotic distribution of the test statistic and investigate the small sample performance by means of...

In this paper we consider autoregressive models with conditional autoregressive variance, including the case of homoscedastic AR-models and the case of ARCH models. Our aim is to test the hypothesis of normality for the innovations in a completely nonparametric way, i. e. without imposing parametric assumptions on the conditional mean and volatilit...

We consider a nonparametric autoregression model under conditional heteroscedasticity with the aim to test whether the innovation distribution changes in time. To this end we develop an asymptotic expansion for the sequential empirical process of nonparametrically estimated innovations (residuals). We suggest a Kolmogorov-Smirnov statistic based on...

We consider the problem of testing significance of predictors in multivariate nonparametric quantile regression. A stochastic process is proposed, which is based on a comparison of the responses with a nonparametric quantile regression estimate under the null hypothesis. It is demonstrated that under the null hypothesis this process converges weakl...

. We consider a general non-parametric regression model, where the distribution of the error, given the covariate, is modelled by a conditional distribution function. For the estimation, a kernel approach as well as the (kernel based) empirical likelihood method are discussed. The latter method allows for incorporation of additional information on...

In this article we propose a new test for additivity in nonparametric quantile regression with a high dimensional predictor. Asymptotic normality of the corresponding test statistic (after appropriate standardization) is established under the null hypothesis, local and fixed alternatives. We also propose a bootstrap procedure which can be used to i...

This paper is concerned with testing rationality restrictions using quantile regression methods. Specifically, we consider negative semidefiniteness of the Slutsky matrix, arguably the core restriction implied by utility maximization. We consider a heterogeneous population characterized by a system of nonseparable structural equations with infi nit...

R code used for conducting the simulations. 'pcrsim' of package 'qpcR' is the workhorse function that creates simulated data starting from the fitted value, adding a desired noise structure and testing different sigmoidal models on the perturbed data. 'code' collects the results and summarizes the data as shown in this manuscript. R script file for...

Mathematical derivation and concise discussion of features and pitfalls in the use of R2 in nonlinear regression and description of the simulation setup.

It is long known within the mathematical literature that the coefficient of determination R(2) is an inadequate measure for the goodness of fit in nonlinear models. Nevertheless, it is still frequently used within pharmacological and biochemical literature for the analysis and interpretation of nonlinear fitting to data. The intensive simulation ap...

In this paper we consider the estimation of the error distribution in a heteroscedastic nonparametric regression model with multivariate covariates. As estimator we consider the empirical distribution function of residuals, which are obtained from multivariate local polynomial fits of the regression and variance functions, respectively. Weak conver...

We propose several new tests for monotonicity of regression functions based on different empirical processes of residuals. The residuals are obtained from recently developed simple kernel based estimators for increasing regression functions based on increasing rearrangements of unconstrained nonparametric estimators. The test statistics are estimat...

In general the empirical likelihood method can improve the performance of estimators by including additional information about the underlying data distribution. Application of the method to kernel density estimation based on independent and identically distributed data always improves the estimation in second order. In this paper we consider estima...

In this article we present a simple procedure to test for the null hypothesis of equality of two regression curves versus one-sided alternatives in a general nonparametric and heteroscedastic setup. The test is based on the comparison of the sample averages of the estimated residuals in each regression model under the null hypothesis. The test stat...

Several testing procedures are proposed that can detect change-points in the error distribution of non-parametric regression models. Different settings are considered where the change-point either occurs at some time point or at some value of the covariate. Fixed as well as random covariates are considered. Weak convergence of the suggested differe...

We propose a new test for independence of error and covariate in a nonparametric regression model. The test statistic is based on a kernel estimator for the L2-distance between the conditional distribution and the unconditional distribution of the covariates. In contrast to tests so far available in literature, the test can be applied in the import...

The aim of this paper is to prove the validity of smooth residual bootstrap versions of procedures that are based on the empirical process of residuals estimated from a non-parametric regression model. From this result, consistency of various model tests in non-parametric regression is deduced, such as goodness-of-fit tests for the regression and v...

We describe how to test the null hypothesis that errors from two para-metrically specified regression models have the same distribution versus a general alternative. First we obtain the asymptotic properties of test-statistics derived from the difference between the two residual-based em-pirical distribution functions. Under the null distribution t...

The aim of this paper is to show that existing estimators for the error distribution in nonparametric regression models can be improved when additional information about the distribution is included by the empirical likelihood method. The weak convergence of the resulting new estimator to a Gaussian process is shown and the performance is investiga...

In this paper, we consider estimating the error distribution in a non-parametric regression model by a smooth version of the empirical distribution function of residuals. We show that a classical residual bootstrap version of the resulting residual-based empirical process joins the same limiting distribution. From this result, consistency of variou...

In the common non-parametric regression model the problem of testing for the parametric form of the conditional variance is considered. A stochastic process based on the difference between the empirical processes that are obtained from the standardized non-parametric residuals under the null hypothesis (of a specific parametric form of the variance...

The purpose of this paper was to propose a procedure for testing the equality of several regression curves "f"_"i" in non-parametric regression models when the noise is inhomogeneous and heteroscedastic, i.e. when the variances depend on the regressor and may vary between groups. The presented approach is very natural because it transfers...

Recently, Dette et al. [A simple nonparametric estimator of a strictly increasing regression function. Bernoulli 12, 469–490] proposed a new monotone estimator for strictly increasing nonparametric regression functions and proved asymptotic normality. We explain two modifications of their method that can be used to obtain monotone versions of any n...

For the problem of testing symmetry of the error distribution in a nonparametric regression model we propose as a test statistic the difference between the two empirical distribution functions of estimated residuals and their counterparts with opposite signs. The weak convergence of the difference process to a Gaussian process is shown. The covaria...

Imagine we have two different samples and are interested in doing semi- or non-parametric regression analysis in each of them, possibly on the same model. In this paper, we consider the problem of testing whether a specific covariate has different impacts on the regression curve in these two samples. We compare the regression curves of different sa...

A new method for monotone estimation of a regression function is proposed, which is potentially attractive to users of conventional smoothing methods. The main idea of the new approach is to construct a density estimate from the estimated values [math] ( [math] ) of the regression function and to use these `data' for the calculation of an estimate...

The objective of this paper is to estimate a bivariate density nonparametrically from a dataset from the joint distribution and datasets from one or both marginal distributions. We develop a copula-based solution, which has potential benefits even when the marginal datasets are empty. For example, if the copula density is sufficiently smooth in the...

In this paper a new method for monotone estimation of a regression function is proposed. The estimator is obtained by the combination of a density and a regression estimate and is appealing to users of conventional smoothing methods as kernel estimators, local polynomials, series estimators or smoothing splines. The main idea of the new approach is...

The aim of this paper is to show that existing estimators for the error distribution in nonparametric regression models can be improved when additional information about the distribution is included by the empirical likelihood method. The weak convergence of the resulting new estimator to a Gaussian process is shown and the performance is investiga...

Assume we have a dataset, Z say, from the joint distribution of random variables X and Y , and two further, independent datasets, X and Y, from the marginal distributions of X and Y , respectively. We wish to combine X, Y and Z, so as to construct an estimator of the joint density. This problem is readily solved in some parametric circumstances. Fo...

Recently, Dette, Neumeyer and Pilz (2005a) proposed a new monotone estimator for strictly increasing nonparametric regression functions and proved asymptotic normality. We explain two modifications of their method that can be used to obtain monotone versions of any nonparametric function estimators, for instance estimators of densities, variance fu...

In the classical linear regression model the problem of testing for symmetry of the error distribution is considered. The test statistic is a functional of the difference between the two empirical distribution functions of the estimated residuals and their counterparts with opposite signs. The weak convergence of the difference process to a Gaussia...

For the common binary response model we propose a direct method for the nonparametric estimation of the effective dose level ED? (0 < ? < 1). The estimator is obtained by the composition of a nonparametric estimate of the quantile response curve and a classical density estimate. The new method yields a simple and reliable monotone estimate of the e...

We describe how to test the null hypothesis that errors from two parametrically specified regression models have the same distribution versus a general alternative. First we obtain the asymptotic properties of teststatistics derived from the difference between the two residual-based empirical distribution functions. Under the null distribution they...

In this paper collections of two-sample U-statistics are considered as a U-process indexed by a class of kernels. Sufficient conditions for a functional central limit theorem in the non-degenerate case are given and a uniform law of large numbers is obtained. The conditions are in terms of random covering numbers and are, for example, fulfilled for...

The purpose of this paper is to propose a procedure for testing the equality of several regression curves f_i in nonparametric regression models when the noise is inhomogeneous. This extends work of Dette and Neumeyer (2001) and it is shown that the new test is asymptotically uniformly more powerful. The presented approach is very natural because i...

In this paper we investigate several tests for the hypothesis of a parametric form of the error distribution in the common linear and nonparametric regression model, which are based on empirical processes of residuals. It is well known that tests in this context are not asymptotically distribution-free and the parametric bootstrap is applied to dea...

We propose a new test for the comparison of two regression curves that is based on a difference of two marked empirical processes based on residuals. The large sample behavior of the corresponding statistic is studied to provide a full nonparametric comparison of regression curves. In contrast to most procedures suggested in the literature, the new...

In the classical linear regression model the problem of testing for symmetry of the error distribution is considered. The test statistic is a functional of the difference between the two empirical distribution functions of the estimated residuals and their counterparts with opposite signs. The weak convergence of the difference process to a Gaussia...

In a recent paper Ahmad and Li (1996) proposed a new test for symmetry of the error distribution in linear regression models and proved asymptotic normality for the distribution of the corresponding test statistic under the null hypothesis and consistency under xed alternatives. The present paper has three purposes. On the one hand we derive the as...

In der vorliegenden Arbeit wird ein neuer Test auf Gleichheit von Regressionsfunktionen zweier nichtparametrischer Regressionsmodelle mit unabhängigen Fehlern vorgestellt. Die Teststatistik basiert auf einem gewichteten empirischen Prozeß, welcher mit Hilfe von unter der Nullhypothese der Gleichheit der Regressionsfunktionen gebildeten Residuen kon...

In the problem of testing the equality of k regression curves from independent samples we discuss three methods using nonparametric estimation techniques of the regression function. The first test is based on a linear combination of estimators for the integrated variance function in the individual samples and in the combined sample. The second appr...

In a recent paper, J. X. Zheng [J. Nonparametric Stat. 7, No. 4, 297–306 (1997; Zbl 1003.62519)] proposed a new specification test of independence between two random vectors by the kernel method. He showed asymptotic normality under the hypothesis and local alternatives. The present work investigates the asymptotic distribution of the corresponding...

We propose a new test for the comparison of two regression curves, which is based on a difference of two marked empirical processes based on residuals. The large sample behaviour of the corresponding statistic is studied to provide a full nonparametric comparison of regression curves. In contrast to most procedures suggested in the literature the n...