On the asymptotic efficiency of the multisample location-scale rank tests and their adjustment for ties
Kybernetika (2007)
- Volume: 43, Issue: 3, page 279-306
- ISSN: 0023-5954
Access Full Article
top
Abstract
topHow to cite
topRublík, František. "On the asymptotic efficiency of the multisample location-scale rank tests and their adjustment for ties." Kybernetika 43.3 (2007): 279-306. <http://eudml.org/doc/33858>.
@article{Rublík2007,
abstract = {Explicit formulas for the non-centrality parameters of the limiting chi-square distribution of proposed multisample rank based test statistics, aimed at testing the hypothesis of the simultaneous equality of location and scale parameters of underlying populations, are obtained by means of a general assertion concerning the location-scale test statistics. The finite sample behaviour of the proposed tests is discussed and illustrated by simulation estimates of the rejection probabilities. A modification for ties of a class of multisample location and scale test statistics, based on ranks and including the proposed test statistics, is presented. It is shown that under the validity of the null hypothesis these modified test statistics are asymptotically chi-square distributed provided that the score generating functions fulfill the imposed regularity conditions. An essential assumption is that the matrix, appearing in these conditions, is regular. Conditions sufficient for the validity of this assumption are also included.},
author = {Rublík, František},
journal = {Kybernetika},
keywords = {multisample rank test for location and scale; asymptotic non- centrality parameter; Pitman–Noether efficiency; adjustment for ties; tables; multisample rank test for location and scale; asymptotic non-centrality parameter; Pitman-Noether efficiency; adjustment for ties},
language = {eng},
number = {3},
pages = {279-306},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On the asymptotic efficiency of the multisample location-scale rank tests and their adjustment for ties},
url = {http://eudml.org/doc/33858},
volume = {43},
year = {2007},
}
TY - JOUR
AU - Rublík, František
TI - On the asymptotic efficiency of the multisample location-scale rank tests and their adjustment for ties
JO - Kybernetika
PY - 2007
PB - Institute of Information Theory and Automation AS CR
VL - 43
IS - 3
SP - 279
EP - 306
AB - Explicit formulas for the non-centrality parameters of the limiting chi-square distribution of proposed multisample rank based test statistics, aimed at testing the hypothesis of the simultaneous equality of location and scale parameters of underlying populations, are obtained by means of a general assertion concerning the location-scale test statistics. The finite sample behaviour of the proposed tests is discussed and illustrated by simulation estimates of the rejection probabilities. A modification for ties of a class of multisample location and scale test statistics, based on ranks and including the proposed test statistics, is presented. It is shown that under the validity of the null hypothesis these modified test statistics are asymptotically chi-square distributed provided that the score generating functions fulfill the imposed regularity conditions. An essential assumption is that the matrix, appearing in these conditions, is regular. Conditions sufficient for the validity of this assumption are also included.
LA - eng
KW - multisample rank test for location and scale; asymptotic non- centrality parameter; Pitman–Noether efficiency; adjustment for ties; tables; multisample rank test for location and scale; asymptotic non-centrality parameter; Pitman-Noether efficiency; adjustment for ties
UR - http://eudml.org/doc/33858
ER -
References
top- Conover W. J., Rank tests for one sample, two samples, and samples without the assumption of a continuous distribution function, Ann. Statist. 1 (1973), 1105–1125 (1973) Zbl0275.62042MR0350953
- Conover W. J., Practical Nonparametric Statistics, Wiley, New York 1999
- Chernoff H., Savage I. R., Asymptotic normality and efficiency of certain non-parametric test statistics, Ann. Math. Statist. 29 (1958), 972–994 (1958) MR0100322
- 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 Mathematical Statistics and Probability (J. Neyman and L. Le Cam, eds.), Berkeley, University of California Press 1967, Vol. 1, pp. 609–638 (1967) MR0214193
- Hájek J., Šidák, Z., Sen P. K., Theory of Rank Tests, Academic Press, San Diego 1999 Zbl0944.62045MR1680991
- Hájek J., A Course in Nonparametric Statistics, Holden Day, San Fransisco, Calif. 1969 Zbl0193.16901MR0246467
- Hollander M., Wolfe D. A., Nonparametric Statistical Methods, Wiley, New York 1999 Zbl0997.62511MR1666064
- Lepage Y., A combination of Wilcoxon’s and Ansari–Bradley’s statistics, Biometrika 58 (1971), 213–217 (1971) Zbl0218.62039MR0408101
- Pratt J. W., On interchanging limits and integrals, Ann. Math. Statist. 31 (1960), 74–77 (1960) Zbl0090.26802MR0123673
- Puri M. L., Sen P. K., Nonparametric Methods in Multivariate Analysis, Wiley, New York 1971 Zbl0237.62033MR0298844
- Rao C. R., Mitra S. K., Generalised Inverse of Matrices and its Applications, Wiley, New York 1971 MR0338013
- Rublík F., The multisample version of the Lepage test, Kybernetika 41 (2005), 713–733 MR2193861
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.