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Rand R. Wilcox - One of the best experts on this subject based on the ideXlab platform.

  • Within Groups ANOVA When Using a Robust Multivariate Measure of Location
    Journal of Modern Applied Statistical Methods, 2016
    Co-Authors: Rand R. Wilcox, Timothy Hayes
    Abstract:

    For robust measures of location associated with J dependent groups, various methods have been proposed that are aimed at testing the global hypothesis of a common measure of location applied to the marginal distributions. A criticism of these methods is that they do not deal with outliers in a manner that takes into account the overall structure of the data. Location Estimators have been derived that deal with outliers in this manner, but evidently there are no simulation results regarding how well they perform when the goal is to test the some global hypothesis. The paper compares four bootstrap methods in terms of their ability to control the Type I error probability when the sample size is small, two of which were found to perform poorly. The choice of location Estimator was found to be important as well. Indeed, for several of the Estimators considered here, control over the Type I error probability was very poor. Only one Estimator performed well when using the first of two general approaches that might be used. It is based on a variation of the (affine equivariant) Donoho-Gasko trimmed mean. For the second general approach, only a Skipped Estimator performed reasonably well. (It removes outliers via a projection method and averages the remaining data.) Only one bootstrap method was found to perform well when using the first approach. A different bootstrap method is recommended when using the second approach.

  • The Small-Sample Efficiency of Some Recently Proposed Multivariate Measures of Location
    2016
    Co-Authors: Rand R. Wilcox
    Abstract:

    Numerous multivariate robust measures of location have been proposed and many have been found to be unsatisfactory in terms of their small-sample efficiency. Several new measures of location have recently been derived, however, nothing is known about their small-sample efficiency or how they compare to the sample mean under normality. This research compared the efficiency for p = 2, 5, and 8 with sample sizes n = 20 and 50 for p-variate data. Although previous studies indicate that so-called Skipped Estimators are efficient, this study found that variations of this approach can perform poorly when n is small and p exceeds 5. One of the best Estimators was found to be a Skipped Estimator where outliers detected by a projection method are eliminated. The TBS, OGK and RMBA Estimators were included and; in some cases, they performed well, however, serious exceptions were identified suggesting that a skippe

  • INVITED ARTICLES Multivariate Location: Robust Estimators And Inference
    2016
    Co-Authors: Rand R. Wilcox, H. J. Keselman
    Abstract:

    The sample mean can have poor efficiency relative to various alternative Estimators under arbitrarily small departures from normality. In the multivariate case, (affine equivariant) Estimators have been proposed for dealing with this problem, but a comparison of various Estimators by Massé and Plante (2003) indicated that the small-sample efficiency of some recently derived methods is rather poor. This article reports that a Skipped mean, where outliers are removed via a projection-type outlier detection method, is found to be more satisfactory. The more obvious method for computing a confidence region based on the Skipped Estimator (using a slight modification of the method in Liu & Singh, 1997) is found to be unsatisfactory except in the bivariate case, at least when the sample size is small. A much more effective method is to use the Bonferroni inequality in conjunction with a standard percentile bootstrap technique applied to the marginal distributions

  • The small-sample efficiency of some recently proposed multivariate measures of location
    Journal of Modern Applied Statistical Methods, 2010
    Co-Authors: Rand R. Wilcox
    Abstract:

    Numerous multivariate robust measures of location have been proposed and many have been found to be unsatisfactory in terms of their small-sample efficiency. Several new measures of location have recently been derived, however, nothing is known about their small-sample efficiency or how they compare to the sample mean under normality. This research compared the efficiency for p = 2, 5, and 8 with sample sizes n = 20 and 50 for p-variate data. Although previous studies indicate that so-called Skipped Estimators are efficient, this study found that variations of this approach can perform poorly when n is small and p exceeds 5. One of the best Estimators was found to be a Skipped Estimator where outliers detected by a projection method are eliminated. The TBS, OGK and RMBA Estimators were included and; in some cases, they performed well, however, serious exceptions were identified suggesting that a Skipped Estimator based on a projection-type outlier detection method is preferable based on efficiency.

  • Multivariate Location: Robust Estimators And Inference
    Journal of Modern Applied Statistical Methods, 2004
    Co-Authors: Rand R. Wilcox, H. J. Keselman
    Abstract:

    It has long been known that under arbitrarily small departures from normality, the sample mean can have poor efficiency relative to various alternative Estimators. In the multivariate case, (affine equivariant) Estimators have been proposed for dealing with this problem, but a comparison of various Estimators by Masse and Plante (2003) indicates that the small-sample efficiency of some recently derived methods is rather poor. This article reports that a Skipped mean, where outliers are removed via a projection-type outlier detection method, is found to be more satisfactory. The more obvious method for computing a confidence region based on the Skipped Estimator (using a slight modification of the method in Liu & Singh, 1997) is found to be unsatisfactory except in the bivariate case, at least when the sample size is small. A much more effective method is to use the Bonferroni inequality in conjunction with a standard percentile bootstrap technique applied to the marginal distributions.

H. J. Keselman - One of the best experts on this subject based on the ideXlab platform.

  • INVITED ARTICLES Multivariate Location: Robust Estimators And Inference
    2016
    Co-Authors: Rand R. Wilcox, H. J. Keselman
    Abstract:

    The sample mean can have poor efficiency relative to various alternative Estimators under arbitrarily small departures from normality. In the multivariate case, (affine equivariant) Estimators have been proposed for dealing with this problem, but a comparison of various Estimators by Massé and Plante (2003) indicated that the small-sample efficiency of some recently derived methods is rather poor. This article reports that a Skipped mean, where outliers are removed via a projection-type outlier detection method, is found to be more satisfactory. The more obvious method for computing a confidence region based on the Skipped Estimator (using a slight modification of the method in Liu & Singh, 1997) is found to be unsatisfactory except in the bivariate case, at least when the sample size is small. A much more effective method is to use the Bonferroni inequality in conjunction with a standard percentile bootstrap technique applied to the marginal distributions

  • Multivariate Location: Robust Estimators And Inference
    Journal of Modern Applied Statistical Methods, 2004
    Co-Authors: Rand R. Wilcox, H. J. Keselman
    Abstract:

    It has long been known that under arbitrarily small departures from normality, the sample mean can have poor efficiency relative to various alternative Estimators. In the multivariate case, (affine equivariant) Estimators have been proposed for dealing with this problem, but a comparison of various Estimators by Masse and Plante (2003) indicates that the small-sample efficiency of some recently derived methods is rather poor. This article reports that a Skipped mean, where outliers are removed via a projection-type outlier detection method, is found to be more satisfactory. The more obvious method for computing a confidence region based on the Skipped Estimator (using a slight modification of the method in Liu & Singh, 1997) is found to be unsatisfactory except in the bivariate case, at least when the sample size is small. A much more effective method is to use the Bonferroni inequality in conjunction with a standard percentile bootstrap technique applied to the marginal distributions.

  • INVITED ARTICLES Multivariate Location: Robust Estimators And Inference
    2004
    Co-Authors: Rand R. Wilcox, H. J. Keselman
    Abstract:

    The sample mean can have poor efficiency relative to various alternative Estimators under arbitrarily small departures from normality. In the multivariate case, (affine equivariant) Estimators have been proposed for dealing with this problem, but a comparison of various Estimators by Masse and Plante (2003) indicated that the small-sample efficiency of some recently derived methods is rather poor. This article reports that a Skipped mean, where outliers are removed via a projection-type outlier detection method, is found to be more satisfactory. The more obvious method for computing a confidence region based on the Skipped Estimator (using a slight modification of the method in Liu & Singh, 1997) is found to be unsatisfactory except in the bivariate case, at least when the sample size is small. A much more effective method is to use the Bonferroni inequality in conjunction with a standard percentile bootstrap technique applied to the marginal distributions.

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

  • The small-sample efficiency of some recently proposed multivariate measures of location
    'United States Sports Academy', 2010
    Co-Authors: Rr Wilcox, Ng M
    Abstract:

    Numerous multivariate robust measures of location have been proposed and many have been found to be unsatisfactory in terms of their small-sample efficiency. Several new measures of location have recently been derived, however, nothing is known about their small-sample efficiency or how they compare to the sample mean under normality. This research compared the efficiency for p = 2, 5, and 8 with sample sizes n = 20 and 50 for p-variate data. Although previous studies indicate that so-called Skipped Estimators are efficient, this study found that variations of this approach can perform poorly when n is small and p exceeds 5. One of the best Estimators was found to be a Skipped Estimator where outliers detected by a projection method are eliminated. The TBS, OGK and RMBA Estimators were included and; in some cases, they performed well, however, serious exceptions were identified suggesting that a Skipped Estimator based on a projection-type outlier detection method is preferable based on efficiency. © 2010 JMASM, Inc.link_to_subscribed_fulltex

Rr Wilcox - One of the best experts on this subject based on the ideXlab platform.

  • The small-sample efficiency of some recently proposed multivariate measures of location
    'United States Sports Academy', 2010
    Co-Authors: Rr Wilcox, Ng M
    Abstract:

    Numerous multivariate robust measures of location have been proposed and many have been found to be unsatisfactory in terms of their small-sample efficiency. Several new measures of location have recently been derived, however, nothing is known about their small-sample efficiency or how they compare to the sample mean under normality. This research compared the efficiency for p = 2, 5, and 8 with sample sizes n = 20 and 50 for p-variate data. Although previous studies indicate that so-called Skipped Estimators are efficient, this study found that variations of this approach can perform poorly when n is small and p exceeds 5. One of the best Estimators was found to be a Skipped Estimator where outliers detected by a projection method are eliminated. The TBS, OGK and RMBA Estimators were included and; in some cases, they performed well, however, serious exceptions were identified suggesting that a Skipped Estimator based on a projection-type outlier detection method is preferable based on efficiency. © 2010 JMASM, Inc.link_to_subscribed_fulltex

Keselman H. J. - One of the best experts on this subject based on the ideXlab platform.

  • Multivariate Location: Robust Estimators And Inference
    DigitalCommons@WayneState, 2004
    Co-Authors: Wilcox, Rand R., Keselman H. J.
    Abstract:

    The sample mean can have poor efficiency relative to various alternative Estimators under arbitrarily small departures from normality. In the multivariate case, (affine equivariant) Estimators have been proposed for dealing with this problem, but a comparison of various Estimators by Massé and Plante (2003) indicated that the small-sample efficiency of some recently derived methods is rather poor. This article reports that a Skipped mean, where outliers are removed via a projection-type outlier detection method, is found to be more satisfactory. The more obvious method for computing a confidence region based on the Skipped Estimator (using a slight modification of the method in Liu & Singh, 1997) is found to be unsatisfactory except in the bivariate case, at least when the sample size is small. A much more effective method is to use the Bonferroni inequality in conjunction with a standard percentile bootstrap technique applied to the marginal distributions