• Journal of the Korean Data and Information Science Society
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• v.24 no.6
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• pp.1401-1408
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• 2013

Kim and Kim (1992) proposed typical nonparametric method for umbrella alternative in randomized block design with replications. In this paper, We consider a test procedure for umbrella alternatives in a randomized block design using extension of the two sample placement tests described in Orban and Wolfe (1982) and treatment tests described in Kim (1999). We perform a Monte Carlo study to compare the empirical powers of the test statistics for underlying distributions.

• Communications for Statistical Applications and Methods
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• v.19 no.6
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• pp.781-791
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• 2012

A $2{\times}2$ Cross-over design is widely used in clinical trials for comparison studies of two kinds of drugs or medical treatments. This design has many statistical methods such as Hills-Armitage's (1979) method or Koch's (1972) method. In this paper, we propose a nonparametric test for $2{\times}2$ Cross-over design based on a two-sample test suggested by Baumgartner et al. (1998). In addition, a Monte Carlo simulation study is adapted to compare the power of the proposed methods with those of previous methods.

• Communications for Statistical Applications and Methods
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• v.27 no.4
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• pp.397-412
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• 2020

In this paper, a notion of data depth is used to propose nonparametric multivariate two sample tests for difference between scale parameters. Data depth can be used to measure the centrality or outlying-ness of the multivariate data point relative to data cloud. A difference in the scale parameters indicates the difference in the depth values of a multivariate data point. By observing this fact on a depth vs depth plot (DD-plot), we propose nonparametric multivariate two sample tests for scale parameters of multivariate distributions. The p-values of these proposed tests are obtained by using Fisher's permutation approach. The power performance of these proposed tests has been reported for few symmetric and skewed multivariate distributions with the existing tests. Illustration with real-life data is also provided.

• Communications for Statistical Applications and Methods
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• v.26 no.1
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• pp.57-67
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• 2019

Income distribution is a major concern in economic theory. In regional economics, it is often of interest to compare income distributions in different regions. Traditional methods often compare the income inequality of different regions by assuming parametric forms of the income distributions, or using summary statistics like the Gini coefficient. In this paper, we propose a nonparametric procedure to test for heterogeneity in income distributions among different regions, and a K-means clustering procedure for clustering income distributions based on energy distance. In simulation studies, it is shown that the energy distance based method has competitive results with other common methods in hypothesis testing, and the energy distance based clustering method performs well in the clustering problem. The proposed approaches are applied in analyzing data from China Health and Nutrition Survey 2011. The results indicate that there are significant differences among income distributions of the 12 provinces in the dataset. After applying a 4-means clustering algorithm, we obtained the clustering results of the income distributions in the 12 provinces.

• The Korean Journal of Applied Statistics
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• v.15 no.2
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• pp.355-366
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• 2002

Nonparametric statistical inference for the parameter of logit model were examined. Usually nonparametric approach is milder than parametric approach based on normal theory assumption. We compared the two nonparametric methods for legit model, the bootstrap and random permutation in the sense of coverage probability. Monte Carlo simulation is conducted for small sample cases. Empirical power of hypothesis test and coverage probability for confidence interval estimation were presented for simple and multiple legit model respectively. An example were also introduced.

• Communications for Statistical Applications and Methods
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• v.30 no.1
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• pp.109-117
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• 2023

Intuitively, a test with more assumptions has greater power than a test with fewer assumptions. This kind of examples are abundant in the nonparametric tests vs corresponding parametric ones. In general, the nonparametric tests are less efficient in terms of asymptotic relative efficiency (ARE) compared to corresponding parametric tests (Daniel, 1990). However, this is not always true. To test equal means under independent normal samples, the usual test involves using the t-distribution with the pooled estimator of the common variance. Adding the assumption of equal sample size, we may derive another test. In this case, two tests using more assumptions were performed for univariate (multivariate) cases. For these examples, it was found that the power function of a test with more assumptions is less than or equal to that of a test with fewer assumptions. This finding can be used as an expository example in master's mathematical statistics courses.

• The Korean Journal of Applied Statistics
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• v.21 no.1
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• pp.19-33
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• 2008

Linear regression method, proposed by Haseman and Elston(1972), for detecting linkage to a quantitative trait of sib pairs is a linkage testing method for a single locus and a single trait. However, multivariate methods for detecting linkage are needed, when information from each of several traits that are affected by the same major gene are available on each individual. Amos et al. (1990) extended the regression method of Haseman and Elston(1972) to incorporate observations of two or more traits by estimating the principal component linear function that results in the strongest correlation between the squared pair differences in the trait measurements and identity by descent at a marker locus. But, it is impossible to control the probability of type I errors with this method at present, since the exact distribution of the statistic that they use is yet unknown. In this paper, we propose a multivariate nonparametric trend test for detecting linkage to multiple traits. We compared with a simulation study the efficiencies of multivariate nonparametric trend test with those of the method developed by Amos et al. (1990) for quantitative traits data. For multivariate nonparametric trend test, the results of the simulation study reveal that the Type I error rates are close to the predetermined significance levels, and have in general high powers.

• Journal of Korean Institute of Industrial Engineers
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• v.12 no.2
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• pp.101-108
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• 1986

Computer programs for IBM PC/XT/AT or compatibles, are presented for running 9 nonparametric tests. They include sign test, Wilcoxon signed rank test, Mann-Whitney Wilcoxon test, Kruskal-Wallis test, Kolmogorov-Smirnov one sample and two sample tests, Kendall and Spearman rank correlation coefficient tests, and Chi square test for contingency table. Each program is written with BASIC language and is combined into a statistical package, 'NONPARA'. It is easily accessible through the menu programs. The alogorithms on which each test is based, are also explained and 3 examples are given.

• Journal of Korean Society for Quality Management
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• v.18 no.1
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• pp.29-39
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• 1990

In this paper we propose a nonparametric test for testing the equality of several regression lines against ordered alternatives, when the independent variables are positive and all regression lines have a common intercept. The proposed test is based on a Jonckheere-type statistic applied to residuals. Under some conditions our proposed test statistic is asymptotically distribution-free. The small-sample powers of our test are compared with other tests by a Monte Carlo study. The simulation results show that the proposed test has significantly higher empirical powers than the other tests considered in this paper.

• Proceedings of the Korean Reliability Society Conference
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• 2004.07a
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• pp.167-175
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• 2004

A nonparametric procedure is proposed to test the exponentiality against the hypothesis that one life distribution has a greater residual life times than the other life distribution. Such a hypothesis turns out to be equivalent to the one that one failure rate is greater than the other and so the proposed test works as a competitor to more IFR tests by Kochar (1979, 1981) and Cheng (1985). Our test statistic utilizes the U-statistics theory and a large sample nonpara metric test is established. The power of the proposed test is discussed by calculating the Pitman asymptotic relative efficiencies against several alter native hypotheses. A numerical example is presented to exemplify the proposed test.