A Note on the Two-Sample Tests under the Normality

박효일 한국자료분석학회 2018 Journal of the Korean Data Analysis Society Vol.20 No.2

In this research, we consider two-sample problems for testing equality between two means. Before proposing new tests, we review briefly the two-sample t-test and Welch- Satterswaite t-test. Then under the normality assumption, we derive the likelihood ratio function without the assumption for equality between two population variances. Then we propose the likelihood ratio test with asymptotic distribution and permutation distributions for the null distribution of the likelihood ratio statistic. By decomposing the likelihood ratio statistic into two types of statistics, we propose another tests using the combination functions and the permutation principle. In order to compare efficiency among tests, we perform the simulation study and obtain the empirical powers with various continuous distributions. We comments on the assumption for the underlying distribution and a possible detour for the violation of assumption as concluding remarks.

Estimation of the treatment effect for the survival time data

박효일 한국통계학회 2013 Journal of the Korean Statistical Society Vol.42 No.2

In this paper, we propose a nonparametric estimation procedure for the treatment effect by applying the least square method for the survival time data. We derive an explicit formula for the estimate which is also easy to compute. Then we discuss the consistency and asymptotic normality for the estimate under several assumptions. Then we illustrate our procedure with a numerical example and compare performance by carrying out a simulation study. Finally we discuss some interesting aspects for the estimation procedure as concluding remarks.

A comparison study of the nonparametric tests based on the empirical distributions

박효일 통계청 2015 통계연구 Vol.20 No.3

In this study, we propose a nonparametric test based on the empirical distribution and its quantile function and compare its performance with the well-known tests for the two-sample problem. For this, first of all, we review some existing nonparametric tests and then propose a new one. We consider to apply the permutation principle to obtain the null distribution. Then we show an example and compare the performance by obtaining empirical powers through a simulation study. Finally, we discuss briefly the re-sampling methods and comment about importance of the continuity assumption for the underlying distribution for the nonprametric test.

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.

통합관리도에 대한 고찰

박효일,유준범,조동현 한국자료분석학회 2017 Journal of the Korean Data Analysis Society Vol.19 No.5

이 연구는 평균과 분산의 통합관리도에 대한 논의를 하고자 한다. 3차원의 자료를 2차원 평면에 표현하기가 어렵기 때문에 통합관리도에 대한 논의는 가설검정과 관리도의 구축에 대한 관계를 이용하여 전개할 것이다. 가설검정과 관리도와의 관계는 다음과 같이 예를 이용하여 간단하게 요약할 수 있다. 정규분포 하에서 유의수준 0.00267 하여 평균에 대한 양쪽검정을 실시하는 경우에 귀무가설이 기각된다면 3-sigma 관리한계선을 가지는 bar{X}-관리도에서는 공정이 관리한계선을 벗어났다는 것을 의미하며 역으로 bar{X}-관리도에서 3-sigma 관리한계선 내에 존재한다면 유의수준 0.00267 하에서 양쪽검정의 결과 귀무가설이 기각되지 않음을 의미한다. 따라서 가설검정과 관리도에 대한 이러한 상호관계를 이용하여 3차원의 자료를 2차원의 평면에 표현하기 어려운 경우에 평균과 분산에 대한 통합검정절차를 사용하여 통합관리도를 구축하는 것이다. 이렇게 구축된 다양한 통합관리도 사이의 효율성을 비교하기 위하여 모의실험을 통한 경험적 ARL을 구하여 통합관리도간의 효율성을 비교한다. 마지막으로 통합관리도와 통합검정절차의 흥미로운 점을 토의하고 장래의 연구방향에 관하여 간단히 언급한다. In this study, we discuss the combined charts for the mean and variance. Since it is difficult to represent three dimensional data on the two dimensional plane, we consider using the equivalence relation between hypothesis testing and control chart. The equivalence relation between the hypothesis testing and control chart can be summarized in the following way using an example. Suppose that we take a two-sided test for the mean using the sample mean under the assumption of normality with the significance level, 0.00267. If the null hypothesis is rejected, then this means that it is out-of-control for the bar{X}-chart which uses the 3-sigma control limit. Also if it is in-control for the bar{X}-chart with 3-sigma control limit, then this means that the null hypothesis cannot be rejected with the significance level, 0.00267. Therefore we should construct the combined chart for the mean and variance using the simultaneous test. Then we compare the efficiency among the combined charts by obtaining empirical ARL through a simulation study. Finally, we discuss some interesting features related with the combined chart and simultaneous test and briefly comment on the future research topic.

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.

Regression Quantile에 대한 고찰

박효일 청주대학교 산업과학연구소 2005 産業科學硏究 Vol.22 No.3

In this study, we consider to review another methodology to estimate the regression coefficient when the distribution of error term may not be normal. The methodology to be reviewed here is called the regression quantile and can be considered as an extension of the method which obtains a sample median. Especially, we emphasize the calculation aspect to obtain the estimate of the regression coefficient using an example and comment briefly asymptotic normality of the estimate. Finally, we discuss some concluding remarks in the conclusion.

A Nonparametric Test under the Proportional Hazards Model

박효일 한국자료분석학회 2016 Journal of the Korean Data Analysis Society Vol.18 No.4

In this research, we propose a nonparametric test procedure under the proportional hazards assumption for the two-sample problem setting. For this, first of all, we review the functional equation for relative risk between the survival and cumulative functions under the proportional hazards model and the estimate of the relative risk proposed by Park, Hong (2007) with the expressions of the empirical ones for the computational convenience. Then we propose a nonparametric test procedure with the null distribution for the test statistic. For obtaining the null distribution, we apply the large sample approximation theorem and derive the asymptotic normality. Then we compare the performance of our proposed test with that of Begun (1987) with the exponential and Weibull distributions, which are frequently applied in the survival analysis by varying sample sizes. We show that our proposed test procedure can be an excellent alternative to the Begun’s one. Finally we discuss some interesting features of our procedure including re-sampling methods to obtain the null distributions of the test statistics as concluding remarks.

A study on the bi-aspect procedure with location and scale parameters (Short Title: Bi-aspect procedure)

박효일,김주성 통계청 2012 통계연구 Vol.17 No.1

In this research we propose a new nonparametric test based on the bi-aspect procedure. We consider the hypothesis which deals with the location and scale parameters simultaneously and propose a new test statistic by choosing a suitable combining function. Then we consider to obtain the p-values by applying the permutation principle. We compare the efficiency among the combining functions by obtaining empirical powers through a simulation study. Then we discuss some interesting results in our procedure as concluding remarks.

A note on score statistic for grouped data

박효일 한국통계학회 2009 Journal of the Korean Statistical Society Vol.38 No.4

In this paper, we consider modifying the score statistic proposed by Prentice and Gloeckler [Prentice, R. L., & Gloeckler, L. A. (1978). Regression analysis of grouped data with applications to breast cancer data. Biometrics, 34, 5767] for the grouped data under the proportional hazards model. For this matter, we apply the likelihood method and derive the scores without re-parameterization as a discrete model. Then we illustrate the test with an example and compare the efficiency with the test of Prentice and Gloeckler's statistic by obtaining empirical powers through simulation study. Also we discuss some possible extension and estimated variances of the score statistic as concluding remarks.