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Comparison Study of Nonparametric Tests for Two-Sample Problem through Simulation
박효일 한국자료분석학회 2014 Journal of the Korean Data Analysis Society Vol.16 No.3
In this paper, we propose a new nonparametric test for two sample problem based on the empirical distribution and its quantile functions when any assumptions for the underlying distribution can not be assumed and compare its performance with the similar tests whose statistics are based on the empirical distribution functions. For this, first of all, we review some existing nonparametric tests and then propose a new one. We consider to obtain the null distribution by applying the permutation principle, which is a resampling method. Then we show an example and compare the performance among the nonparametric tests with our test by obtaining empirical powers through a simulation study under the location translation alternative. Also we discuss the bootstrap method which is another resampling method to obtain the null distribution of test statistics. Finally, we comment briefly about the importance of the continuity assumption for the underlying distribution and the topic of our future research.
Nonparametric Tests for Multiple Endpoints with Grouped Observations
박효일,홍승만 한국자료분석학회 2008 Journal of the Korean Data Analysis Society Vol.10 No.1
In this paper, we consider a nonparametric test procedure for the multiple endpoints with grouped data under two sample problem setting. For the construction of the test statistic, we use the linear rank statistics which were derived based on the likelihood ratio principle for each component. Then the asymptotic distribution of the test statistic is derived under the null hypothesis. Finally, we illustrate our test procedure with an example and discuss some concluding remarks.
박효일 청주대학교 산업과학연구소 2003 産業科學硏究 Vol.21 No.1
In this paper, we consider applying the permutation principle to the testing procedures in parametric and nonparametric aspects. For this study, we use an artificial data for numerical illustration Finally we discuss some aspects about permutation tests and compare with bootstrap method
A Nonparametric Test Procedure for Multivariate Censored Data
박효일 한국자료분석학회 2007 Journal of the Korean Data Analysis Society Vol.9 No.4
In this paper, we consider a nonparametric test procedure for comparing two distribution functions based on the multivariate, grouped and right censored data under the two sample problem setting. For the construction of the test statistic, we use the linear rank statistics which were derived based on the likelihood ratio principle for each component. Then the asymptotic distribution of the test statistic is derived under the null hypothesis. Finally, we illustrate our test with an example and discuss some concluding remarks. In appendix, we derive the expression of the covariance.
박효일 청주대학교 2009 産業科學硏究 Vol.27 No.1
In this study, we review some aspect about semi-parametric models, which are extensively used in the survival analysis and reliability theory. For the review in this paper among the semi-parametric model, we consider mainly the proportional hazards model and additive hazards model. Also we include the accelerated time model to compare some properties with them. Then we close this paper with some concluding remarks for possible future study and suggesting new directions of study for the multivariate case
박효일 청주대학교 2010 産業科學硏究 Vol.28 No.1
In this study, we review to compare the permutation principle with the bootstrap method. The permutation principle re-samples without replacement but the bootstrap method does with replacement. We proceed our arguments with an example to show and provide some concrete pictures to the readers with providing SAS/IML program to help check the both procedures. Then we discuss some interesting phenomena in our arguments and comment on some facts for both methods as concluding remarks.
A Study on the Nonparametric Tests for the Two-Sample Problem
박효일 한국자료분석학회 2010 Journal of the Korean Data Analysis Society Vol.12 No.5
In this paper, we consider nonparametric test procedures based on a group of quantile test statistics. Since we do not assume any specific model, this new nonparametric tests may be useful when the underlying distributions are completely unknown. We consider the quadratic form of statistic for the general alternatives and derive the chi-square distribution as the limiting distribution for the large sample case. Then we illustrate our procedure with an example and compare the proposed tests with the individual quantile tests by obtaining empirical powers through simulation study by applying the permutation principle. Also we comment on the related discussions to this testing procedure as concluding remarks.
A Note on the Likelihood Ratio Simultaneous Multivariate Tests
박효일 한국자료분석학회 2018 Journal of the Korean Data Analysis Society Vol.20 No.3
In this study, we propose the simultaneous tests for the mean vector and covariance matrix for the multivariate normal data. For this, first of all, we drive the likelihood ratio function and obtain the asymptotic distribution for the two times of the log likelihood ratio function with the likelihood ratio arguments. Then we propose a likelihood ratio simultaneous test for the mean vector and covariance matrix. Also for obtaining the null distribution of the likelihood ratio function, we consider the Monte-Carlo method which depends completely upon the computer facility and its softwares. Then the Monte-Carlo method may yield the exact likelihood ratio simultaneous test. Then we illustrate our procedure with a numerical example and compare efficiency among proposed tests with the combination tests under the various scenarios for the mean vector and covariance matrix by obtaining empirical powers through a simulation study. Finally, we discuss some interesting features for the proposed simultaneous tests with related topics and a method for obtaining the likelihood ratio statistics.
A Discussion for Test of Covariance Matrix with Likelihood Ratio Principle
박효일 한국자료분석학회 2017 Journal of the Korean Data Analysis Society Vol.19 No.6
In this study, we consider to discuss and propose a test procedure for covariance matrix under the normality assumption. For this purpose, first of all, we identify that the likelihood ratio function consists of a product of likelihood ratio functions of individual eigenvalues of covariance matrix. Then we construct a union-intersection type of statistic based on the minimum among individual p-values and propose a test. We note that the null distributions of the individual statistics are all chi-square and independent. Since the union-intersection test statistic is one of combination functions, we propose two more tests using the combination functions by combining p-values of individual partial tests. Then we compare the efficiency of the proposed tests with the asymptotic one by obtaining empirical powers through a simulation study. For this simulation study, we include the likelihood ratio test with chi-square which is the limiting distribution of the likelihood ratio statistic. Finally, we discuss some interesting features related with the test for the covariance matrix.
박효일 청주대학교 2012 産業科學硏究 Vol.30 No.1
In this study, we consider reviewing two kinds of process capability indices based on the mean which are famous and useful in the production floor to control and improve the production process in the industry. Then we introduce another definition of the process capability index which uses a median of the process distribution. Also we propose its estimate, discuss the consistency of the estimate and derive the asymptotic normality with the corresponding estimate of the limiting variance. Then we discuss some interesting features of the process capability indices with the re-sampling method as concluding remarks.