• 응용통계연구
• /
• 제19권2호
• /
• pp.241-256
• /
• 2006

EDF에 근거한 $Cram{\acute{e}}r$-von Mises 통계량을 합교원리를 이용하여 다변량으로 일반화한다. 그리고 제안된 통계량의 귀무가설에서의 극한분포를 적절한 공분산 함수를 가진 가우스 과정의 적분의 형태로 표현하고 통계량의 근사적인 계산방법을 고려한다. 또한 실제 자료에 제안된 통계량을 적용해보고 여러가지 대립가설에서의 검정력을 유사한 통계량과 비교해 본다.

• 한국통계학회:학술대회논문집
• /
• 한국통계학회 2003년도 춘계 학술발표회 논문집
• /
• pp.191-197
• /
• 2003

This paper considers the independence test for two stationary infinite order autoregressive processes. For a test, we follow the empirical process method devised by Hoeffding (1948) and Blum, Kiefer and Rosenblatt (1961), and construct the Cram${\acute{e}}$r-von Mises type test statistics based on the least squares residuals. It is shown that the proposed test statistics behave asymptotically the same as those based on true errors.

• Communications for Statistical Applications and Methods
• /
• 제24권5호
• /
• pp.519-531
• /
• 2017

We consider goodness-of-fit test statistics for Weibull distributions when data are randomly censored and the parameters are unknown. Koziol and Green (Biometrika, 63, 465-474, 1976) proposed the $Cram\acute{e}r$-von Mises statistic's randomly censored version for a simple hypothesis based on the Kaplan-Meier product limit of the distribution function. We apply their idea to the other statistics based on the empirical distribution function such as the Kolmogorov-Smirnov and Liao and Shimokawa (Journal of Statistical Computation and Simulation, 64, 23-48, 1999) statistics. The latter is a hybrid of the Kolmogorov-Smirnov, $Cram\acute{e}r$-von Mises, and Anderson-Darling statistics. These statistics as well as the Koziol-Green statistic are considered as test statistics for randomly censored Weibull distributions with estimated parameters. The null distributions depend on the estimation method since the test statistics are not distribution free when the parameters are estimated. Maximum likelihood estimation and the graphical plotting method with the least squares are considered for parameter estimation. A simulation study enables the Liao-Shimokawa statistic to show a relatively high power in many alternatives; however, the null distribution heavily depends on the parameter estimation. Meanwhile, the Koziol-Green statistic provides moderate power and the null distribution does not significantly change upon the parameter estimation.

• Communications for Statistical Applications and Methods
• /
• 제26권5호
• /
• pp.431-443
• /
• 2019

Goodness-of-fit techniques are an important topic in statistical analysis. Censored data occur frequently in survival experiments; therefore, many studies are conducted when data are censored. In this paper we mainly consider test statistics based on the empirical distribution function (EDF) to test normal distributions with unknown location and scale parameters when data are randomly censored. The most famous EDF test statistic is the Kolmogorov-Smirnov; in addition, the quadratic statistics such as the $Cram{\acute{e}}r-von$ Mises and the Anderson-Darling statistic are well known. The $Cram{\acute{e}}r-von$ Mises statistic is generalized to randomly censored cases by Koziol and Green (Biometrika, 63, 465-474, 1976). In this paper, we generalize the Anderson-Darling statistic to randomly censored data using the Kaplan-Meier estimator as it was done by Koziol and Green. A simulation study is conducted under a particular censorship model proposed by Koziol and Green. Through a simulation study, the generalized Anderson-Darling statistic shows the best power against almost all alternatives considered among the three EDF statistics we take into account.

• Communications for Statistical Applications and Methods
• /
• 제23권3호
• /
• pp.215-230
• /
• 2016

The powers of some tests for independence hypothesis against positive (negative) quadrant dependence in generalized Farlie-Gumbel-Morgenstern distribution are compared graphically by simulation. Some of these tests are usual linear rank tests of independence. Two other possible rank tests of independence are locally most powerful rank test and a powerful nonparametric test based on the $Cram{\acute{e}}r-von$ Mises statistic. We also evaluate the empirical power of the class of distribution-free tests proposed by Kochar and Gupta (1987) based on the asymptotic distribution of a U-statistic and the test statistic proposed by $G{\ddot{u}}ven$ and Kotz (2008) in generalized Farlie-Gumbel-Morgenstern distribution. Tests of independence are also compared for sample sizes n = 20, 30, 50, empirically. Finally, we apply two examples to illustrate the results.

• 응용통계연구
• /
• 제24권5호
• /
• pp.883-891
• /
• 2011

수명시간에 대한 모형으로 로그정규분포가 자주 사용되며, 이는 자료의 변환에 의하여 정규성 검정과 동일한 문제로 생각할 수 있다. 따라서 자료의 로그정규성 검정을 위하여, 정규성 검정에 자주 이용되는 Shapiro-Wilk 형태의 검정통계량을 Kaplan-Meier의 product limit 경험분포함수를 이용하여 임의중도절단자료로 일반화한다. Cram er von Mises 통계량을 임의중도절단자료로 일반화한 Koziol과 Green (1976)의 통계량과 비교하였으며 이를 위하여 단순귀무가설을 가정하였다. 중도절단분포에 대한 모형으로는 Koziol과 Green (1976)에서 제시한 모형과 이와 유사한 다른 모형 두 가지를 고려하였다. 검정력 비교 결과 제시한 통계량이 로그정규성 또는 정규성 검정에 더 좋은 검정력을 보여주었으며 검정력은 중도절단분포 모형보다는 자료의 중도절단비율에 영향을 받는다는 것을 볼 수 있었다.

• 응용통계연구
• /
• 제30권4호
• /
• pp.513-528
• /
• 2017

두 표본 집단이 동일한 분포를 따르는지 비교하기 위해 분포무관 검정이 많이 사용된다. 하지만 여러 검정법을 체계적으로 비교한 연구가 존재하지 않아서 각 검정법의 특성을 고려하여 연구 상황에 맞는 검정법을 선택하기가 어려웠다. 본 연구에서는 이표본 분포 동일성 검정에 해당하는 여러 분포무관 검정법들을 소개하고 체계적인 모의실험을 통해 그 성능을 비교하고자 한다. 두 표본이 각각 (1) 위치, (2) 척도, (3) 왜도, (4) 첨도, (5) 꼬리가중치가 다른 분포에서 추출된 상황에 대해 실험하였다. 실험 결과를 바탕으로 이표본 분포 동일성 검정법 사용에 대한 실용적인 지침을 제시하려고 한다.

• Communications for Statistical Applications and Methods
• /
• 제25권2호
• /
• pp.217-234
• /
• 2018

Copulas are a tool for constructing multivariate distributions and formalizing the dependence structure between random variables. From copula literature review, there are a few asymmetric copulas available so far while data collected from the real world often exhibit asymmetric nature. This necessitates developing asymmetric copulas. In this study, we discuss a method to construct a new class of bivariate asymmetric copulas based on products of symmetric (sometimes asymmetric) copulas with powered arguments in order to determine if the proposed construction can offer an added value for modeling asymmetric bivariate data. With these newly constructed copulas, we investigate dependence properties and measure of association between random variables. In addition, the test of symmetry of data and the estimation of hyper-parameters by the maximum likelihood method are discussed. With two real example such as car rental data and economic indicators data, we perform the goodness-of-fit test of our proposed asymmetric copulas. For these data, some of the proposed models turned out to be successful whereas the existing copulas were mostly unsuccessful. The method of presented here can be useful in fields such as finance, climate and social science.