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Refined approximations to permutation tests for multivariate inference. (English) Zbl 0875.62183
Summary: Various authors have proposed approximations to permutation tests of independence between two data tables. We develop approximations based on explicit expressions of the first three moments of three different test statistics under the permutation distribution. The rejection level is then determined by using a Pearson-type III distribution matching the values of the first three moments. We present three examples in which the relative merits of the test statistics are examined and the results of the approximation procedure are compared with explicit permutation tests.

MSC:
62G10 Nonparametric hypothesis testing
62H15 Hypothesis testing in multivariate analysis
Software:
SAS; Canoco
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[1] Biondini, M. E.; Mielke, P. W.; Redente, E. F.: Permutation techniques based on Euclidean analysis: a new and powerful statistical method for ecological research. Coenoses 3, 155-174 (1988)
[2] Box, G. E. P.; Watson, G. S.: Robustness to nonnormality of regression tests. Biometrika 49, 93-106 (1962) · Zbl 0113.34901
[3] Chessel, D.; Mercier, P.: Couplage de tableaux statistiques et liaisons espèces – environment. Biométrie et environment, 15-43 (1993)
[4] Edgington, E. S.: Randomization tests. (1987) · Zbl 0629.62003
[5] Escoufier, Y.: Le traitement des variables vectorielles. Biometrics 29, 751-760 (1973)
[6] Giri, N. C.: Multivariate statistical inference. 249-256 (1977) · Zbl 0374.62052
[7] Gittins, R.: Ecological applications of canonical analysis. Multivariate methods in ecological work (1979) · Zbl 0445.49014
[8] Hall, P.: On the removal of skewness by transformation. J of the roy. Statist. soc., B 54, 221-228 (1992)
[9] Hitier, S.: Quelques éléments pour tester l’indépendance de deax tableaux de données. D.E.A. report (1993)
[10] Kazi-Aoual, F.: Approximations to permutation tests for data analysis. Rapport de recherche no 93-06 (1993)
[11] Kazi-Aoual, F.; Sabatier, R.; Lebreton, J. D.: Approximation of permutation tests for multivariate inference. Applications to species environment relationships. Proc. 2nd French-Japanese statistical meeting (1992)
[12] Krishnaiah, P. R.: Handbook of statistics, vol. 1, analysis of variance. 1 (1980) · Zbl 0456.62041
[13] Lazraq, A.: Inférence sur plusieurs mesures de liaison entre deux vecteurs aléatoires et algorithmes de sélection de variables. Ph.d. thesis (1988)
[14] Lebreton, J. D.; Roux, M.; Bacou, A. M.; Banco, G.: Bioméco (Biométrie-ecologie), verson 3.9. Software of statistical ecology for PC (1990)
[15] Lebreton, J. D.; Sabatier, R.; Banco, G.; Bacou, A. M.: Principal component and correspondence analysis with respect to environmental variables: an overview of their role in studies of structure-activity and species-environment relationships. Applied multivariate analysis in SAR and environmental studies, 85-114 (1991)
[16] Mcdonald, L. L.: A discussion of robust procedures in multivariate analysis. USDA forest service, general technical report RM-87, 242-244 (1981)
[17] Manly, B. F. J.: Randomization and Monte-Carlo methods in biology. (1991) · Zbl 0726.92001
[18] Mardia, K. V.: The effect of nonnormality on some multivariate tests and robustness to nonnormality in the linear model. Biometrika 58, No. 1, 105-122 (1971) · Zbl 0218.62081
[19] Mielke, P. W.: Clarification and appropriate inferences for mantel and valand’s nonparametric multivariate analysis technique. Biometrics 34, 277-282 (1978) · Zbl 0401.62046
[20] Mielke, P. W.: Commun. statist.. No. 11, 847 (1979)
[21] Mielke, P. W.; Berry, K. J.; Brier, G. W.: Application of multiresponse permutation procedures for examining seasonal changes in monthly mean sea-level pressure patterns. Monthly weather rev. 109, 120-126 (1981)
[22] Mielke, P. W.; Berry, K. J.; Johnson, E. S.: Multiresponse permutatioon procedures for a priori classifications. Commun. statist., No. 5, 1409-1424 (1976) · Zbl 0358.62039
[23] Pillai, K. C. S.: Some new tests criteria in multivariate analysis. Ann. math. Statist. 26, 117-121 (1955) · Zbl 0064.13801
[24] Pillai, K. C. S.; Jayachandran, K.: On the exact distribution of pillai’s \(V(s)\) criterion. J. amer. Statist. assoc. 65, 447-454 (1970)
[25] Rao, C. R.: The use and interpretation of principal component analysis in applied research. Sankhya ser A. 26, 329-359 (1964) · Zbl 0137.37207
[26] Raz, J.; Fein, G.: Testing for heterogeneity of evoked potentials signals using an approximation to an exact permutation test. Biometrics 48, 1069-1080 (1992)
[27] Sabatier, R.; Lebreton, J. D.; Chessel, D.: Principal component analysis with instrumental variables as a tool for modelling composition data. Multiway data analysis, 341-352 (1989)
[28] Institute, Sas: SAS user’s guide; statistics. (1985)
[29] Stewart, D.; Love, W.: A general canonical correlation index. Psychol. bull. 70, No. 3, 160-163 (1968)
[30] Braak, C. J. F. Ter: The analysis of vegetation-environment relationships by canonical correspondence analysis. Vegetatio 69, 69-77 (1987)
[31] Braak, C. J. F. Ter: Canoco, a Fortran program for canonical community ordination by (partial) (detiended) (canonical) correspondence analysis, principal component analysis.. (1987)
[32] Tucker, L. R.: An inter-battery method of factor analysis. Psychometrika 23, 111-136 (1958) · Zbl 0097.35102
[33] Wollenberg, A. L. V.D.: Redundancy analysis, an alternative for canonical correlation analysis. Psychometrika 42, 207-221 (1977) · Zbl 0354.92050
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