The multisample version of the Lepage test

František Rublík

Kybernetika (2005)

  • Volume: 41, Issue: 6, page [713]-733
  • ISSN: 0023-5954

Abstract

top
The two-sample Lepage test, devised for testing equality of the location and scale parameters against the alternative that at least for one of the parameters the equality does not hold, is extended to the general case of k > 1 sampled populations. It is shown that its limiting distribution is the chi-square distribution with 2 ( k - 1 ) degrees of freedom. This k -sample statistic is shown to yield consistent test and a formula for its noncentrality parameter under Pitman alternatives is derived. For some particular alternatives, the power of the k -sample test is compared with the power of the Kruskal–Wallis test or with the power of the Ansari–Bradley test by means of simulation estimates. Multiple comparison methods for detecting differing populations, based on this multisample version of the Lepage test or on the multisample version of the Ansari–Bradley test, are also constructed.

How to cite

top

Rublík, František. "The multisample version of the Lepage test." Kybernetika 41.6 (2005): [713]-733. <http://eudml.org/doc/33783>.

@article{Rublík2005,
abstract = {The two-sample Lepage test, devised for testing equality of the location and scale parameters against the alternative that at least for one of the parameters the equality does not hold, is extended to the general case of $k>1$ sampled populations. It is shown that its limiting distribution is the chi-square distribution with $2(k-1)$ degrees of freedom. This $k$-sample statistic is shown to yield consistent test and a formula for its noncentrality parameter under Pitman alternatives is derived. For some particular alternatives, the power of the $k$-sample test is compared with the power of the Kruskal–Wallis test or with the power of the Ansari–Bradley test by means of simulation estimates. Multiple comparison methods for detecting differing populations, based on this multisample version of the Lepage test or on the multisample version of the Ansari–Bradley test, are also constructed.},
author = {Rublík, František},
journal = {Kybernetika},
keywords = {multisample rank test for location and scale; Lepage statistic; consistency; non-centrality parameter; multiple comparisons for location and scale parameters; multisample rank test; consistency; noncentrality parameter},
language = {eng},
number = {6},
pages = {[713]-733},
publisher = {Institute of Information Theory and Automation AS CR},
title = {The multisample version of the Lepage test},
url = {http://eudml.org/doc/33783},
volume = {41},
year = {2005},
}

TY - JOUR
AU - Rublík, František
TI - The multisample version of the Lepage test
JO - Kybernetika
PY - 2005
PB - Institute of Information Theory and Automation AS CR
VL - 41
IS - 6
SP - [713]
EP - 733
AB - The two-sample Lepage test, devised for testing equality of the location and scale parameters against the alternative that at least for one of the parameters the equality does not hold, is extended to the general case of $k>1$ sampled populations. It is shown that its limiting distribution is the chi-square distribution with $2(k-1)$ degrees of freedom. This $k$-sample statistic is shown to yield consistent test and a formula for its noncentrality parameter under Pitman alternatives is derived. For some particular alternatives, the power of the $k$-sample test is compared with the power of the Kruskal–Wallis test or with the power of the Ansari–Bradley test by means of simulation estimates. Multiple comparison methods for detecting differing populations, based on this multisample version of the Lepage test or on the multisample version of the Ansari–Bradley test, are also constructed.
LA - eng
KW - multisample rank test for location and scale; Lepage statistic; consistency; non-centrality parameter; multiple comparisons for location and scale parameters; multisample rank test; consistency; noncentrality parameter
UR - http://eudml.org/doc/33783
ER -

References

top
  1. Ansari A. R., Bradley R. A., 10.1214/aoms/1177705688, Ann. Math. Statist. 31 (1960), 1174–1189 (1960) MR0117835DOI10.1214/aoms/1177705688
  2. Chernoff H., Savage I. R., 10.1214/aoms/1177706436, Ann. Math. Statist. 29 (1958), 972–994 (1958) MR0100322DOI10.1214/aoms/1177706436
  3. Conover W. J., Practical Nonparametric Statistics, Wiley, New York 1999 
  4. Critchlow D. E., Fligner M. A., 10.1080/03610929108830487, Commun. Statist. Theory Meth. 20 (1991), 127–139 (1991) MR1114636DOI10.1080/03610929108830487
  5. Goria M. N., Vorlíčková D., On the asymptotic properties of rank statistics for the two-sample location and scale problem, Aplikace matematiky 30 (1985), 425–434 (1985) MR0813531
  6. Govindajarulu Z., Cam, L. Le, Raghavachari M., Generalizations of theorems of Chernoff and Savage on the asymptotic normality of test statistics, In: Proc. Fifth Berkeley Symposium on Math. Statist. and Probab., Vol. 1 (1966) (J. Neyman and L. Le Cam, eds.), Univ. of California Press, Berkeley 1967, pp. 609–638 (1966) MR0214193
  7. Hájek J., Šidák Z., Theory of Rank Tests, Academia, Prague 1967 Zbl0944.62045MR0229351
  8. Harter H. L., 10.1214/aoms/1177705684, Ann. Math. Statist. 31 (1960) 1122–1147 (1960) Zbl0106.13602MR0123384DOI10.1214/aoms/1177705684
  9. Hayter A. J., 10.1214/aos/1176346392, Ann. Statist. 12 (1984), 61–75 (1984) MR0733499DOI10.1214/aos/1176346392
  10. Hollander M., Wolfe D. A., Nonparametric Statistical Methods, Wiley, New York 1999 Zbl0997.62511MR1666064
  11. Koziol J. A., Reid N., 10.1214/aos/1176343998, Ann. Statist. 5 (1977), 1099–1106 (1977) Zbl0391.62053MR0518897DOI10.1214/aos/1176343998
  12. Kruskal W. H., 10.1214/aoms/1177729332, Ann. Math. Statist. 23 (1952), 525–540 (1952) Zbl0048.36703MR0050850DOI10.1214/aoms/1177729332
  13. Kruskal W. H., Wallis W. A., 10.1080/01621459.1952.10483441, J. Amer. Statist. Assoc. 47 (1952), 583–621 (1952) Zbl0048.11703DOI10.1080/01621459.1952.10483441
  14. Lepage Y., 10.1093/biomet/58.1.213, Biometrika 58 (1971), 213–217 (1971) Zbl0218.62039MR0408101DOI10.1093/biomet/58.1.213
  15. Lepage Y., 10.1093/biomet/60.1.113, Biometrika 60 1973), 113–116 (1973) Zbl0256.62041MR0331625DOI10.1093/biomet/60.1.113
  16. Mann H. B., Whitney D. R., 10.1214/aoms/1177730491, Ann. Math. Statist. 18 (1947), 50–60 (1947) MR0022058DOI10.1214/aoms/1177730491
  17. Miller R. G., Jr., Simultaneous Statistical Inference, Second edition. Springer–Verlag, New York – Heidelberg 1985 Zbl0463.62002MR0612319
  18. Puri M. L., 10.1007/BF02868176, Ann. Inst. Stat. Math. 17 (1965), 323–330 (1965) Zbl0161.16202MR0196863DOI10.1007/BF02868176
  19. Puri M. L., Sen P. K., Nonparametric Methods in Multivariate Analysis, Wiley, New York 1971 Zbl0237.62033MR0298844
  20. Rao C. R., Mitra S. K., Generalised Inverse of Matrices and its Applications, Wiley, New York 1971 MR0338013
  21. Rublík F., On optimality of the LR tests in the sense of exact slopes, Part II. Application to individual distributions. Kybernetika 25 (1989), 117–135 (1989) Zbl0692.62016MR0995954
  22. Rublík F., Asymptotic distribution of the likelihood ratio test statistic in the multisample case, Math. Slovaca 49 (1999), 577–598 (1999) Zbl0957.62011MR1746901
  23. Tsai W. S., Duran B. S., Lewis T. O., 10.1080/01621459.1975.10480304, J. Amer. Statist. Assoc. 70 (1975), 791–796 (1975) Zbl0322.62048DOI10.1080/01621459.1975.10480304
  24. Wilcoxon F., 10.2307/3001968, Biometrics Bull. 1 (1945), 80–83 (1945) DOI10.2307/3001968

NotesEmbed ?

top

You must be logged in to post comments.