The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform

Leandro Pardo - One of the best experts on this subject based on the ideXlab platform.

  • a Wald type test statistic based on robust modified median estimator in logistic regression models
    Journal of Statistical Computation and Simulation, 2017
    Co-Authors: Tomas Hobza, Nirian Martin, Leandro Pardo
    Abstract:

    ABSTRACTIn 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 modified median estimator, we also consider a Wald-type test statistic for testing linear hypotheses in the logistic regression model and we obtain its asymptotic distribution under the assumption of random regressors. An extensive simulation study is presented in order to analyse the efficiency as well as the robustness of the modified median estimator and Wald-type test based on it.

  • a Wald type test statistic for testing linear hypothesis in logistic regression models based on minimum density power divergence estimator
    Electronic Journal of Statistics, 2017
    Co-Authors: Ayanendranath Basu, Abhik Ghosh, Abhijit Mandal, Nirian Martin, Leandro Pardo
    Abstract:

    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. A family of robust Wald type tests are considered here, where the minimum density power divergence estimator is used instead of the maximum likelihood estimator. We obtain the asymptotic distribution and also study the robustness properties of these Wald type test statistics. The robustness of the tests is investigated theoretically through the influence function analysis as well as suitable practical examples. It is theoretically established that the level as well as the power of the Wald-type tests are stable against contamination, while the classical Wald type test breaks down in this scenario. Some classical examples are presented which numerically substantiate the theory developed. Finally a simulation study is included to provide further confirmation of the validity of the theoretical results established in the paper.

  • a Wald type test statistic for testing linear hypothesis in logistic regression models based on minimum density power divergence estimator
    arXiv: Statistics Theory, 2016
    Co-Authors: Ayanendranath Basu, Abhik Ghosh, Abhijit Mandal, Nirian Martin, Leandro Pardo
    Abstract:

    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 minimum density power divergence estimator instead of the maximum likelihood estimator and it is referred to as the Wald-type test statistic in the paper. We obtain the asymptotic distribution and also study the robustness properties of the Wald type test statistic. The robustness of the tests is investigated theoretically through the influence function analysis as well as suitable practical examples. It is theoretically established that the level as well as the power of the Wald-type tests are stable against contamination, while the classical Wald type test breaks down in this scenario. Some classical examples are presented which numerically substantiate the theory developed. Finally a simulation study is included to provide further confirmation of the validity of the theoretical results established in the paper.

  • influence analysis of robust Wald type tests
    Journal of Multivariate Analysis, 2016
    Co-Authors: Abhik Ghosh, Abhijit Mandal, Nirian Martin, Leandro Pardo
    Abstract:

    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 influence functions as well as the chi-square inflation factors. It is theoretically established that the level and power of these robust tests are stable against outliers, whereas the classical Wald test breaks down. Some numerical examples confirm the validity of the theoretical results.

Melanie M Wall - One of the best experts on this subject based on the ideXlab platform.

  • small sample adjustments in using the sandwich variance estimator in generalized estimating equations
    Statistics in Medicine, 2002
    Co-Authors: Wei Pan, Melanie M Wall
    Abstract:

    The generalized estimating equation (GEE) approach is widely used in regression analyses with correlated response data. Under mild conditions, the resulting regression coefficient estimator is consistent and asymptotically normal with its variance being consistently estimated by the so-called sandwich estimator. Statistical inference is thus accomplished by using the asymptotic Wald chi-squared test. However, it has been noted in the literature that for small samples the sandwich estimator may not perform well and may lead to much inflated type I errors for the Wald chi-squared test. Here we propose using an approximate t- or F-test that takes account of the variability of the sandwich estimator. The level of type I error of the proposed t- or F-test is guaranteed to be no larger than that of the Wald chi-squared test. The satisfactory performance of the proposed new tests is confirmed in a simulation study. Our proposal also has some advantages when compared with other new approaches based on direct modifications of the sandwich estimator, including the one that corrects the downward bias of the sandwich estimator. In addition to hypothesis testing, our result has a clear implication on constructing Wald-type confidence intervals or regions.

Wei Pan - One of the best experts on this subject based on the ideXlab platform.

  • small sample adjustments in using the sandwich variance estimator in generalized estimating equations
    Statistics in Medicine, 2002
    Co-Authors: Wei Pan, Melanie M Wall
    Abstract:

    The generalized estimating equation (GEE) approach is widely used in regression analyses with correlated response data. Under mild conditions, the resulting regression coefficient estimator is consistent and asymptotically normal with its variance being consistently estimated by the so-called sandwich estimator. Statistical inference is thus accomplished by using the asymptotic Wald chi-squared test. However, it has been noted in the literature that for small samples the sandwich estimator may not perform well and may lead to much inflated type I errors for the Wald chi-squared test. Here we propose using an approximate t- or F-test that takes account of the variability of the sandwich estimator. The level of type I error of the proposed t- or F-test is guaranteed to be no larger than that of the Wald chi-squared test. The satisfactory performance of the proposed new tests is confirmed in a simulation study. Our proposal also has some advantages when compared with other new approaches based on direct modifications of the sandwich estimator, including the one that corrects the downward bias of the sandwich estimator. In addition to hypothesis testing, our result has a clear implication on constructing Wald-type confidence intervals or regions.

Ayanendranath Basu - One of the best experts on this subject based on the ideXlab platform.

  • a Wald type test statistic for testing linear hypothesis in logistic regression models based on minimum density power divergence estimator
    Electronic Journal of Statistics, 2017
    Co-Authors: Ayanendranath Basu, Abhik Ghosh, Abhijit Mandal, Nirian Martin, Leandro Pardo
    Abstract:

    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. A family of robust Wald type tests are considered here, where the minimum density power divergence estimator is used instead of the maximum likelihood estimator. We obtain the asymptotic distribution and also study the robustness properties of these Wald type test statistics. The robustness of the tests is investigated theoretically through the influence function analysis as well as suitable practical examples. It is theoretically established that the level as well as the power of the Wald-type tests are stable against contamination, while the classical Wald type test breaks down in this scenario. Some classical examples are presented which numerically substantiate the theory developed. Finally a simulation study is included to provide further confirmation of the validity of the theoretical results established in the paper.

  • a Wald type test statistic for testing linear hypothesis in logistic regression models based on minimum density power divergence estimator
    arXiv: Statistics Theory, 2016
    Co-Authors: Ayanendranath Basu, Abhik Ghosh, Abhijit Mandal, Nirian Martin, Leandro Pardo
    Abstract:

    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 minimum density power divergence estimator instead of the maximum likelihood estimator and it is referred to as the Wald-type test statistic in the paper. We obtain the asymptotic distribution and also study the robustness properties of the Wald type test statistic. The robustness of the tests is investigated theoretically through the influence function analysis as well as suitable practical examples. It is theoretically established that the level as well as the power of the Wald-type tests are stable against contamination, while the classical Wald type test breaks down in this scenario. Some classical examples are presented which numerically substantiate the theory developed. Finally a simulation study is included to provide further confirmation of the validity of the theoretical results established in the paper.

Nirian Martin - One of the best experts on this subject based on the ideXlab platform.

  • a Wald type test statistic based on robust modified median estimator in logistic regression models
    Journal of Statistical Computation and Simulation, 2017
    Co-Authors: Tomas Hobza, Nirian Martin, Leandro Pardo
    Abstract:

    ABSTRACTIn 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 modified median estimator, we also consider a Wald-type test statistic for testing linear hypotheses in the logistic regression model and we obtain its asymptotic distribution under the assumption of random regressors. An extensive simulation study is presented in order to analyse the efficiency as well as the robustness of the modified median estimator and Wald-type test based on it.

  • a Wald type test statistic for testing linear hypothesis in logistic regression models based on minimum density power divergence estimator
    Electronic Journal of Statistics, 2017
    Co-Authors: Ayanendranath Basu, Abhik Ghosh, Abhijit Mandal, Nirian Martin, Leandro Pardo
    Abstract:

    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. A family of robust Wald type tests are considered here, where the minimum density power divergence estimator is used instead of the maximum likelihood estimator. We obtain the asymptotic distribution and also study the robustness properties of these Wald type test statistics. The robustness of the tests is investigated theoretically through the influence function analysis as well as suitable practical examples. It is theoretically established that the level as well as the power of the Wald-type tests are stable against contamination, while the classical Wald type test breaks down in this scenario. Some classical examples are presented which numerically substantiate the theory developed. Finally a simulation study is included to provide further confirmation of the validity of the theoretical results established in the paper.

  • a Wald type test statistic for testing linear hypothesis in logistic regression models based on minimum density power divergence estimator
    arXiv: Statistics Theory, 2016
    Co-Authors: Ayanendranath Basu, Abhik Ghosh, Abhijit Mandal, Nirian Martin, Leandro Pardo
    Abstract:

    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 minimum density power divergence estimator instead of the maximum likelihood estimator and it is referred to as the Wald-type test statistic in the paper. We obtain the asymptotic distribution and also study the robustness properties of the Wald type test statistic. The robustness of the tests is investigated theoretically through the influence function analysis as well as suitable practical examples. It is theoretically established that the level as well as the power of the Wald-type tests are stable against contamination, while the classical Wald type test breaks down in this scenario. Some classical examples are presented which numerically substantiate the theory developed. Finally a simulation study is included to provide further confirmation of the validity of the theoretical results established in the paper.

  • influence analysis of robust Wald type tests
    Journal of Multivariate Analysis, 2016
    Co-Authors: Abhik Ghosh, Abhijit Mandal, Nirian Martin, Leandro Pardo
    Abstract:

    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 influence functions as well as the chi-square inflation factors. It is theoretically established that the level and power of these robust tests are stable against outliers, whereas the classical Wald test breaks down. Some numerical examples confirm the validity of the theoretical results.