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Ingrid Van Keilegom - One of the best experts on this subject based on the ideXlab platform.

  • a new test for the Parametric form of the variance function in non Parametric Regression
    Journal of The Royal Statistical Society Series B-statistical Methodology, 2007
    Co-Authors: Holger Dette, Natalie Neumeyer, Ingrid Van Keilegom
    Abstract:

    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 function) and the alternative is introduced and its weak convergence established. This result is used for the construction of a Kolmogorov-Smirnov and a Cramer-von Mises type of statistic for testing the Parametric form of the conditional variance. The consistency of a bootstrap approximation is established, and the finite sample properties of this approximation are investigated by means of a simulation study. In particular the new procedure is compared with some of the currently available methods for this problem. Copyright 2007 Royal Statistical Society.

  • A new test for the Parametric form of the variance function in non‐Parametric Regression
    Journal of The Royal Statistical Society Series B-statistical Methodology, 2007
    Co-Authors: Holger Dette, Natalie Neumeyer, Ingrid Van Keilegom
    Abstract:

    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 function) and the alternative is introduced and its weak convergence established. This result is used for the construction of a Kolmogorov-Smirnov and a Cramer-von Mises type of statistic for testing the Parametric form of the conditional variance. The consistency of a bootstrap approximation is established, and the finite sample properties of this approximation are investigated by means of a simulation study. In particular the new procedure is compared with some of the currently available methods for this problem. Copyright 2007 Royal Statistical Society.

Holger Dette - One of the best experts on this subject based on the ideXlab platform.

  • a new test for the Parametric form of the variance function in non Parametric Regression
    Journal of The Royal Statistical Society Series B-statistical Methodology, 2007
    Co-Authors: Holger Dette, Natalie Neumeyer, Ingrid Van Keilegom
    Abstract:

    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 function) and the alternative is introduced and its weak convergence established. This result is used for the construction of a Kolmogorov-Smirnov and a Cramer-von Mises type of statistic for testing the Parametric form of the conditional variance. The consistency of a bootstrap approximation is established, and the finite sample properties of this approximation are investigated by means of a simulation study. In particular the new procedure is compared with some of the currently available methods for this problem. Copyright 2007 Royal Statistical Society.

  • A new test for the Parametric form of the variance function in non‐Parametric Regression
    Journal of The Royal Statistical Society Series B-statistical Methodology, 2007
    Co-Authors: Holger Dette, Natalie Neumeyer, Ingrid Van Keilegom
    Abstract:

    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 function) and the alternative is introduced and its weak convergence established. This result is used for the construction of a Kolmogorov-Smirnov and a Cramer-von Mises type of statistic for testing the Parametric form of the conditional variance. The consistency of a bootstrap approximation is established, and the finite sample properties of this approximation are investigated by means of a simulation study. In particular the new procedure is compared with some of the currently available methods for this problem. Copyright 2007 Royal Statistical Society.

Natalie Neumeyer - One of the best experts on this subject based on the ideXlab platform.

  • A bootstrap version of the residual-based smooth empirical distribution function
    Journal of Nonparametric Statistics, 2008
    Co-Authors: Natalie Neumeyer
    Abstract:

    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 various goodness-of-fit tests in non-Parametric Regression Models is obtained.

  • a new test for the Parametric form of the variance function in non Parametric Regression
    Journal of The Royal Statistical Society Series B-statistical Methodology, 2007
    Co-Authors: Holger Dette, Natalie Neumeyer, Ingrid Van Keilegom
    Abstract:

    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 function) and the alternative is introduced and its weak convergence established. This result is used for the construction of a Kolmogorov-Smirnov and a Cramer-von Mises type of statistic for testing the Parametric form of the conditional variance. The consistency of a bootstrap approximation is established, and the finite sample properties of this approximation are investigated by means of a simulation study. In particular the new procedure is compared with some of the currently available methods for this problem. Copyright 2007 Royal Statistical Society.

  • A new test for the Parametric form of the variance function in non‐Parametric Regression
    Journal of The Royal Statistical Society Series B-statistical Methodology, 2007
    Co-Authors: Holger Dette, Natalie Neumeyer, Ingrid Van Keilegom
    Abstract:

    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 function) and the alternative is introduced and its weak convergence established. This result is used for the construction of a Kolmogorov-Smirnov and a Cramer-von Mises type of statistic for testing the Parametric form of the conditional variance. The consistency of a bootstrap approximation is established, and the finite sample properties of this approximation are investigated by means of a simulation study. In particular the new procedure is compared with some of the currently available methods for this problem. Copyright 2007 Royal Statistical Society.

Hengjian Cui - One of the best experts on this subject based on the ideXlab platform.

Lixing Zhu - One of the best experts on this subject based on the ideXlab platform.

  • Model diagnosis for Parametric Regression in high dimensional spaces
    Biometrika, 2008
    Co-Authors: Winfried Stute, Lixing Zhu
    Abstract:

    SUMMARY We study tools for checking the validity of a Parametric Regression Model. When the dimension of the regressors is large, many of the existing tests face the curse of dimensionality or require some ordering of the data. Our tests are based on the residual empirical process marked by proper functions of the regressors. They are able to detect local alternatives converging to the null at Parametric rates. Parametric and nonParametric alternatives are considered. In the latter case, through a proper principal component decomposition, we are able to derive smooth directional tests which are asymptotically distribution-free under the null Model. The new tests take into account precisely the 'geometry of the Model'. A simulation study is carried through and an application to a real dataset is illustrated.

  • a semi Parametric Regression Model with errors in variables
    Scandinavian Journal of Statistics, 2003
    Co-Authors: Lixing Zhu, Hengjian Cui
    Abstract:

    .  In this paper, we consider a partial linear Regression Model with measurement errors in possibly all the variables. We use a method of moments and deconvolution to construct a new class of Parametric estimators together with a non-Parametric kernel estimator. Strong convergence, optimal rate of weak convergence and asymptotic normality of the estimators are investigated.

  • A Semi-Parametric Regression Model with Errors in Variables
    Scandinavian Journal of Statistics, 2003
    Co-Authors: Lixing Zhu, Hengjian Cui
    Abstract:

    In this paper, we consider a partial linear Regression Model with measurement errors in possibly all the variables. We use a method of moments and deconvolution to construct a new class of Parametric estimators together with a non-Parametric kernel estimator. Strong convergence, optimal rate of weak convergence and asymptotic normality of the estimators are investigated. Copyright 2003 Board of the Foundation of the Scandinavian Journal of Statistics..