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

• Journal of the Korean Statistical Society
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• 제23권1호
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• pp.103-114
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• 1994

For a $2 \times 2$ factorial design without the restriction of a linear model or without regard to error terms having homoscedasticity, under the null hypothesis of no interaction we can have the rank transformed F statistic for interaction converge in distribution to a chi-squared random variable with one degree of random if and only if there is only main effect.

• 응용통계연구
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• 제21권6호
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• pp.933-945
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• 2008

발병연령과 이에 관련되었다고 의심되는 좌위와의 연관성이 실제로 존재하는 경우에 유전자형 정보에 따라 발병연령(age of onset) 분포의 추세가 뚜렷하게 나타난다. 그러나 연관성 검정에서 주로 채택하고 있는 발병연령의 상한연령(cutoff age)을 제한하는 표본추출은 유전자형에 따른 여러 군의 미완결 자료의 분포가 다름을 초래하게 되며, 이러한 미완결 분포 차이는 발병연령의 추세 검정에 있어 효율성을 낮추는 원인이 된다. 일반적으로 두 군의 경우에 그 대책으로써 윌콕슨(Wilcoxon) 통계량보다는 미완결 자료의 분포가 다름에 영향을 덜 받는다고 알려진 로그순위(log-rank) 통계량을 사용한다. 본 논문에서는 로그순위 통계량 적용을 유전자형에 따른 여러 군의 경우로 확장하여 Jones와 Browley (1989)에 언급된 일반화 로그순위 추세 검정통계량(generalized log-rank statistic for trend)을 제안하며, 연관성 연구에서 이 검정통계량과 여러 다른 추세 검정통계량의 효율성을 모의실험으로 알아본다.

• Journal of the Korean Statistical Society
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• 제26권3호
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• pp.319-332
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• 1997

The application of multivariate linear rank statistics to data with item nonresponse is considered. Only a modest extension of the complete data techniques is required when the missing data may be thought of as a random sample, and an appropriate modification of the covariances is derived. A proof of the asymptotic multivariate normality is given. A review of some related results in the literature is presented and applications including longitudinal and repeated measures designs are discussed.

• Journal of the Korean Statistical Society
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• 제23권1호
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• pp.135-149
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• 1994

We discussed a comparison of distribution-free two-sample procedures based on placements or ranks. Iterative asymptotic distribution of both two-sample procedures is studies and small sample Monte Carlo simulation results are presented. Also, we proposed the Hodges-Lehmann type location estimator based on linear placement statistics.

• Communications for Statistical Applications and Methods
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• 제2권2호
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• pp.198-212
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• 1995

This study provides a nonparametric procedure for the statistical inference of the parameters in stationary autoregressive processes. A confidence region and a hypothesis testing procedure based on a class of signed linear rank statistics are proposed and the asymptotic distributions of the test statistic both underthe null hypothesis and under a sequence of local alternatives are investigated. Some desirable asymptotic properties including the asymptotic relative efficiency are discussed for various score functions.

• International Journal of Reliability and Applications
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• 제6권1호
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• pp.53-64
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• 2005

In this paper, we propose a nonparametric test procedure for the multivariate, grouped and right censored data for two sample problem. For the construction of the test statistic, we use the linear rank statistics for each component and apply the permutation principle for obtaining the null distribution. For the large sample case, the asymptotic distribution is derived under the null hypothesis with the additional assumption that two censoring distributions are also equal. Finally, we illustrate our procedure with an example and discuss some concluding remarks. In appendices, we derive the expression of the covariance matrix and prove the asymptotic distribution.

• Genomics & Informatics
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• 제1권2호
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• pp.94-100
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• 2003

Motivation: Many have observed a nonlinear relationship between the signal intensity and the transcript abundance in microarray data. The first step in analyzing the data is to normalize it properly, and this should include a correction for the nonlinearity. The commonly used linear normalization schemes do not address this problem. Results: Nonlinearity is present in both cDNA and oligonucleotide arrays, but we concentrate on the latter in this paper. Across a set of chips, we identify those genes whose within-chip ranks are relatively constant compared to other genes of similar intensity. For each gene, we compute the sum of the squares of the differences in its within-chip ranks between every pair of chips as our statistic and we select a small fraction of the genes with the minimal changes in ranks at each intensity level. These genes are most likely to be non-differentially expressed and are subsequently used in the normalization procedure. This method is a generalization of the rank-invariant normalization (Li and Wong, 2001), using all available chips rather than two at a time to gather more information, while using the chip that is least likely to be affected by nonlinear effects as the reference chip. The assumption in our method is that there are at least a small number of non­differentially expressed genes across the intensity range. The normalized expression values can be substantially different from the unnormalized values and may result in altered down-stream analysis.

• 응용통계연구
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• 제9권1호
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• pp.139-152
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• 1996

확률화 블럭 계획법에서 최적 가중치를 이용한 우산형 대립가설에 대한 비모수검정법을 제안하고자 한다. Mack과 Wolfe(1981) 형태의 통계량에 대한 제안된 통계량의 점근상대효율을 최대로 하는 가중치를 구하고, 이러한 가중치를 가지는 제안된 통계량과 Mack과 Wolfe 형태의 통계량 및 선형 순위 통계량의 점근상대 효율을 고려하였다. 소표본에서 모의 실험을 통하여 블럭의 크기가 다른 경우 제안된 통계량의 검정력이 우수함을 보였다.

• Communications for Statistical Applications and Methods
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• 제12권3호
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• pp.557-587
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• 2005

This paper elucidates the limiting Gaussian distribution of a class of rank order statistics {$T_N$} for two sample problem pertaining to empirical processes of the squared residuals from two independent samples of GARCH processes. A distinctive feature is that, unlike the residuals of ARMA processes, the asymptotics of {$T_N$} depend on those of GARCH volatility estimators. Based on the asymptotics of {$T_N$}, we empirically assess the relative asymptotic efficiency and effect of the GARCH specification for some GARCH residual distributions. In contrast with the independent, identically distributed or ARMA settings, these studies illuminate some interesting features of GARCH residuals.