Multiple Comparison Procedure

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Marvin K Nakayama - One of the best experts on this subject based on the ideXlab platform.

  • single stage Multiple Comparison Procedure for quantiles and other parameters
    Winter Simulation Conference, 2007
    Co-Authors: Marvin K Nakayama
    Abstract:

    We present a single-stage Multiple-Comparison Procedure for comparing parameters of independent systems, where the parameters are not necessarily means or steady-state means. We assume that for each system, the parameter has an estimation process that satisfies a central limit theorem (CLT) and that we have a consistent variance-estimation process for the variance parameter appearing in the CLT. The Procedure allows for unequal run lengths or sample sizes across systems, and also allows for unequal and unknown variance parameters across systems. The Procedure is asymptotically valid as the run lengths or sample sizes of all system grow large. One setting the framework encompasses is comparing quantiles of independent populations. It also covers comparing means or other moments of independent populations, functions of means, and steady-state means of stochastic processes.

  • Winter Simulation Conference - Single-stage Multiple-Comparison Procedure for quantiles and other parameters
    2007 Winter Simulation Conference, 2007
    Co-Authors: Marvin K Nakayama
    Abstract:

    We present a single-stage Multiple-Comparison Procedure for comparing parameters of independent systems, where the parameters are not necessarily means or steady-state means. We assume that for each system, the parameter has an estimation process that satisfies a central limit theorem (CLT) and that we have a consistent variance-estimation process for the variance parameter appearing in the CLT. The Procedure allows for unequal run lengths or sample sizes across systems, and also allows for unequal and unknown variance parameters across systems. The Procedure is asymptotically valid as the run lengths or sample sizes of all system grow large. One setting the framework encompasses is comparing quantiles of independent populations. It also covers comparing means or other moments of independent populations, functions of means, and steady-state means of stochastic processes.

Takashi Seo - One of the best experts on this subject based on the ideXlab platform.

  • Simultaneous Tests for Independence Among Components of Random Vector by Step-Down Multiple Comparison Procedure
    Communications in Statistics - Simulation and Computation, 2012
    Co-Authors: Sho Takahashi, Takahiro Nishiyama, Takashi Seo
    Abstract:

    In this article, we consider testing independence among components of random vector in multivariate normal population. For testing independence, we use the modified likelihood ratio test statistic which is improved an approximation to χ2 distribution of the likelihood ratio test statistic. In order to perform simultaneous tests for independence among components of random vector, we use the step-down Multiple Comparison Procedure based on the closed testing Procedure proposed by Marcus et al. (1976). Finally, we perform Monte Carlo simulations and present numerical results.

  • Testing independence by step-wise Multiple Comparison Procedure
    2010
    Co-Authors: Sho Takahashi, Takahiro Nishiyama, Takashi Seo
    Abstract:

    In this paper, we consider testing independence among components of random vector in multivariate normal population. For testing independence, we use the modied likelihood ratio test statistic which is improved an approximation to 2 distribution of the likelihood ratio test statistic. In order to perform simultaneous tests for independence among components of random vector, we use a step-down Multiple Comparison Procedure based on closed testing Procedure proposed by Marcus, Peritz and Gabriel (1976). Moreover, we construct a step-up Multiple Comparison Procedure for testing independence simultaneously. Finally, we perform Monte Carlo simulations and present numerical results.

  • the multivariate tukey kramer Multiple Comparison Procedure among four correlated mean vectors
    American Journal of Mathematical and Management Sciences, 2008
    Co-Authors: Takahiro Nishiyama, Takashi Seo
    Abstract:

    SYNOPTIC ABSTRACTIn this article, conservative simultaneous confidence intervals for pairwise Comparisons among mean vectors in multivariate normal distributions are considered. In order to give the simultaneous confidence intervals, we need the value of the upper 100α percentile of the T2max·p statistic. However, it is difficult to find the exact value. So, as an approximation Procedure, Seo, Mano and Fujikoshi (1994) proposed the multivariate Tukey-Kramer Procedure which is the multivariate version of Tukey-Kramer Procedure (Tukey (1953); Kramer (1956, 1957)). Also, the multivariate version of the generalized Tukey conjecture has been affirmatively proved in the case of three correlated mean vectors by Seo, Mano and Fujikoshi (1994). In this article the affirmative proof of the multivariate generalized Tukey conjecture in the case of four mean vectors can be completed. Further, the upper bound for the conservativeness of the multivariate Tukey-Kramer Procedure is also given. Finally, numerical results b...

  • A Note on the Conservative Multivariate Tukey-Kramer Multiple Comparison Procedure
    American Journal of Mathematical and Management Sciences, 1996
    Co-Authors: Takashi Seo
    Abstract:

    SYNOPTIC ABSTRACTIn this article, the conservative simultaneous confidence intervals for pairwise Multiple Comparisons among correlated mean vectors including the case of unequal sample sizes are considered. One of the important problems is to evaluate the bound of simultaneous confidence levels for approximate Multiple Comparisons Procedures. For all pairwise Comparisons as a particular case, the multivariate Tukey-Kramer Procedure proposed by Seo, Mano and Fujikoshi(1994) is discussed, and its bound for conservativeness is given by the reduction of the coverage probability. The numerical results by Monte Carlo simulations are presented for the selected parameters.

Takahiro Nishiyama - One of the best experts on this subject based on the ideXlab platform.

  • Simultaneous Tests for Independence Among Components of Random Vector by Step-Down Multiple Comparison Procedure
    Communications in Statistics - Simulation and Computation, 2012
    Co-Authors: Sho Takahashi, Takahiro Nishiyama, Takashi Seo
    Abstract:

    In this article, we consider testing independence among components of random vector in multivariate normal population. For testing independence, we use the modified likelihood ratio test statistic which is improved an approximation to χ2 distribution of the likelihood ratio test statistic. In order to perform simultaneous tests for independence among components of random vector, we use the step-down Multiple Comparison Procedure based on the closed testing Procedure proposed by Marcus et al. (1976). Finally, we perform Monte Carlo simulations and present numerical results.

  • Testing independence by step-wise Multiple Comparison Procedure
    2010
    Co-Authors: Sho Takahashi, Takahiro Nishiyama, Takashi Seo
    Abstract:

    In this paper, we consider testing independence among components of random vector in multivariate normal population. For testing independence, we use the modied likelihood ratio test statistic which is improved an approximation to 2 distribution of the likelihood ratio test statistic. In order to perform simultaneous tests for independence among components of random vector, we use a step-down Multiple Comparison Procedure based on closed testing Procedure proposed by Marcus, Peritz and Gabriel (1976). Moreover, we construct a step-up Multiple Comparison Procedure for testing independence simultaneously. Finally, we perform Monte Carlo simulations and present numerical results.

  • the multivariate tukey kramer Multiple Comparison Procedure among four correlated mean vectors
    American Journal of Mathematical and Management Sciences, 2008
    Co-Authors: Takahiro Nishiyama, Takashi Seo
    Abstract:

    SYNOPTIC ABSTRACTIn this article, conservative simultaneous confidence intervals for pairwise Comparisons among mean vectors in multivariate normal distributions are considered. In order to give the simultaneous confidence intervals, we need the value of the upper 100α percentile of the T2max·p statistic. However, it is difficult to find the exact value. So, as an approximation Procedure, Seo, Mano and Fujikoshi (1994) proposed the multivariate Tukey-Kramer Procedure which is the multivariate version of Tukey-Kramer Procedure (Tukey (1953); Kramer (1956, 1957)). Also, the multivariate version of the generalized Tukey conjecture has been affirmatively proved in the case of three correlated mean vectors by Seo, Mano and Fujikoshi (1994). In this article the affirmative proof of the multivariate generalized Tukey conjecture in the case of four mean vectors can be completed. Further, the upper bound for the conservativeness of the multivariate Tukey-Kramer Procedure is also given. Finally, numerical results b...

  • on the conservative multivariate Multiple Comparison Procedure of correlated mean vectors with a control
    1995
    Co-Authors: Takahiro Nishiyama
    Abstract:

    In this paper, we consider the simultaneous confidence intervals for Multiple Comparisons with a control among mean vectors from the multivariate normal distributions. We discuss the approximate simultaneous confidence Procedure proposed by Seo (1995). Seo (1995) conjectured that this Procedure always construct the conservative approximate simultaneous confidence intervals. In this paper, we give the affirmative proof of this conjecture and give the upper bound for the conservativeness of this Procedure in the case of five correlated mean vectors. Finally, numerical results by Monte Carlo simulation are given.

Tsunehisa Imada - One of the best experts on this subject based on the ideXlab platform.

  • multivariate one sided Multiple Comparison Procedure with a control based on the approximate likelihood ratio test
    Biometrical Journal, 2010
    Co-Authors: Tsunehisa Imada, Yoshiro Yamamoto
    Abstract:

    In this study, we discuss a Multiple Comparison Procedure with a control for multivariate one-sided test in each pairwise Comparison. For pairwise Comparisons, we use the approximate likelihood ratio test statistics derived by Tang et al. (An approximate likelihood ratio test for a normal mean vector with nonnegative components with application to clinical trials. Biometrika 1989, 76, 577-583). We derive a formula to determine the critical value for pairwise Comparisons satisfying a specified significance level. Furthermore, we formulate the power of the test for our Multiple Comparison Procedure. Finally, we give some numerical examples regarding the critical values and the power of the test.

  • Multivariate one‐sided Multiple Comparison Procedure with a control based on the approximate likelihood ratio test
    Biometrical Journal, 2010
    Co-Authors: Tsunehisa Imada, Yoshiro Yamamoto
    Abstract:

    In this study, we discuss a Multiple Comparison Procedure with a control for multivariate one-sided test in each pairwise Comparison. For pairwise Comparisons, we use the approximate likelihood ratio test statistics derived by Tang et al. (An approximate likelihood ratio test for a normal mean vector with nonnegative components with application to clinical trials. Biometrika 1989, 76, 577-583). We derive a formula to determine the critical value for pairwise Comparisons satisfying a specified significance level. Furthermore, we formulate the power of the test for our Multiple Comparison Procedure. Finally, we give some numerical examples regarding the critical values and the power of the test.

  • change point analysis for sequence of normal meansbased on Multiple Comparison Procedure
    International Conference on Innovative Computing Information and Control, 2006
    Co-Authors: Tsunehisa Imada, H Douke
    Abstract:

    In this study we consider change point analysis for a sequence of normal means. Specifically, we construct a Procedure for finding all change points in a single test by using Multiple Comparison Procedure. We determine the critical value for pairwise Comparison for a specified significance level. Then we consider the power of the test for our Multiple compairson Procedure. Finally we give some numerical examples regarding the critical value and the power of the test.

  • ICICIC (1) - Change Point Analysis for Sequence of Normal MeansBased on Multiple Comparison Procedure
    First International Conference on Innovative Computing Information and Control - Volume I (ICICIC'06), 1
    Co-Authors: Tsunehisa Imada, H Douke
    Abstract:

    In this study we consider change point analysis for a sequence of normal means. Specifically, we construct a Procedure for finding all change points in a single test by using Multiple Comparison Procedure. We determine the critical value for pairwise Comparison for a specified significance level. Then we consider the power of the test for our Multiple compairson Procedure. Finally we give some numerical examples regarding the critical value and the power of the test.

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

  • Sequential Multiple Comparison Procedure for Finding a Changing Point in Dose Finding Test
    Studies in Classification Data Analysis and Knowledge Organization, 2009
    Co-Authors: H Douke, Tomohiro Nakamura
    Abstract:

    Changing point analysis in many dose finding tests has been applied to examine the change of a response with increasing dose levels of an experimental compound. In this study, we assume that the group observations at each dose level are sequentially obtain and a response shows a linear tendency at an early stage with increasing dose levels. Then we propose a sequential Multiple Comparison Procedure to identify the minimum effective dose level to first separate from a linear response by sequentially comparing each dose level with the zero dose level. Furthermore, we present a formulation to determine a critical value, the power of the test and a Procedure to determine the necessary sample size in our sequential test.

  • change point analysis for sequence of normal meansbased on Multiple Comparison Procedure
    International Conference on Innovative Computing Information and Control, 2006
    Co-Authors: Tsunehisa Imada, H Douke
    Abstract:

    In this study we consider change point analysis for a sequence of normal means. Specifically, we construct a Procedure for finding all change points in a single test by using Multiple Comparison Procedure. We determine the critical value for pairwise Comparison for a specified significance level. Then we consider the power of the test for our Multiple compairson Procedure. Finally we give some numerical examples regarding the critical value and the power of the test.

  • ICICIC (1) - Change Point Analysis for Sequence of Normal MeansBased on Multiple Comparison Procedure
    First International Conference on Innovative Computing Information and Control - Volume I (ICICIC'06), 1
    Co-Authors: Tsunehisa Imada, H Douke
    Abstract:

    In this study we consider change point analysis for a sequence of normal means. Specifically, we construct a Procedure for finding all change points in a single test by using Multiple Comparison Procedure. We determine the critical value for pairwise Comparison for a specified significance level. Then we consider the power of the test for our Multiple compairson Procedure. Finally we give some numerical examples regarding the critical value and the power of the test.

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