Nonparametric Tests for Multiple Endpoints with Grouped Observations

다국어 초록 (Multilingual Abstract)

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.

참고문헌 (Reference)

1 Wei, L. J., "Two-sample asymptotically distribution-free tests for incomplete multivariate observations" 79 : 653-661, 1984

2 Shaver, R. H., "The Pennsylvanian ostracode Bairdia oklahomaensis in Indiana" 34 : 656-670, 1960

3 Fisher, R. A., "The Design of Experiments" Hafner 1935

4 Bell, C. B., "Some nonparametric tests for multivariate the goodness-of- fit, multisample, incomplete and symmetry problems, Multivariate Analysis-II" Academic Press 1969

5 Good, P., "Permutation test-A pratical guide to resampling methods for testing hypotheses" Springer-Verlag 2000

6 Park, H. I., "Nonparametric rank-order tests for the right censored and grouped data in linear model" 22 : 3143-3158, 1993

7 Puri, M. L., "Nonparametric methods in multivariate analysis" Wiley and Sons, Inc 1971

8 Puri, M. L., "Nonparametric methods in general linear model" Wiley and Sons, Inc 1985

9 Schilling, M. F., "Multivariate two-sample tests based on nearest neighbors" 81 : 799-806, 1986

10 Pesarin, F, "Multivariate permutation tests with application in Biostatistics" Wiley and Sons, Inc 2001

11 Park, H. I., "Multivariate percentile tests for incomplete data" 54 : 934-944, 2002

12 Friedman, "Multivariate generalizations of the Wald-Wolfowitz and Smirnov two-sample tests" 7 : 697-717, 1979

13 Mardia, K. V., "Multivariate analysis" Academic press 1979

14 Bickel, P. J., "Mathematical Statistics" Holden-Day Inc 1977

15 Heitijan, P., "Inference from grouped continuous data:a review" 4 : 164-183, 1989

16 김명근, "Detection of Outliers in Multivariate Regression Using Plug-in Method" 한국자료분석학회 7 (7): 1117-1124, 2005

17 Neuhaus, "Conditional rank tests for the two-sample problem under random censorship" 21 : 1760-1779, 1993

18 Efron, B., "Bootstrap methods: another look at the jackknife" 7 : 1-26, 1979

19 C. Christopher Lee, "Applied Multivariate Statistical Analysis in Sports: A Case of Boxing" 한국자료분석학회 6 (6): 613-623, 2004

20 Henze, N., "A multivariate two-sample test based on the number of nearest neighbor type coincidence" 16 : 772-783, 1988

21 Park, H. I., "A multivariate control median test" 79 : 123-139, 1999

22 Bickel, P. J., "A distribution free version of the Smirnov two sample test in the p-variate case" 40 : 1-23, 1969

23 Chung, K. L., "A course in probability theory, second edition" Academic Press 1974

24 박효일, "A Nonparametric Test Procedure for Multivariate Censored Data" 한국자료분석학회 9 (9): 1589-1599, 2007

25 정강모, "A Detection Method of Multivariate Outliers using Decompositions of the Squared Mahalanobis Distance" 한국자료분석학회 7 (7): 1935-1943, 2005