In this paper, we consider profile analysis for the observations with two-step monotone missing data. There exist three interesting hypotheses - the parallelism hypothesis, level hypothesis, and flatness hypothesis - when comparing the profiles of some groups. The T²-type statistics and their asymptotic null distributions for the three hypotheses are given for two-sample profile analysis. We propose the approximate upper percentiles of these test statistics. When the data do not have missing observations, the test statistics perform lower than the usual test statistics, for example, as in [8]. Further, we consider a parallel profile model for several groups when the data have two-step monotone missing observations. Under the assumption of non-missing data, the likelihood ratio test procedure is derived by [16]. We derive the test statistic based on the likelihood ratio. Finally, in order to investigate the accuracy for the null distributions of the proposed statistics, we perform a Monte Carlo simulation for some selected parameters values.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1153,
author = {Mizuki Onozawa and Sho Takahashi and Takashi Seo},
title = {Tests for profile analysis based on two-step monotone missing data},
journal = {Discussiones Mathematicae Probability and Statistics},
volume = {33},
year = {2013},
pages = {171-190},
zbl = {1320.62130},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1153}
}
Mizuki Onozawa; Sho Takahashi; Takashi Seo. Tests for profile analysis based on two-step monotone missing data. Discussiones Mathematicae Probability and Statistics, Tome 33 (2013) pp. 171-190. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1153/
[000] [1] T.W. Anderson and I. Olkin, Maximum-likelihood estimation of the parameters of a multivariate normal distribution, Linear Algebra and its Appl. 70 (1985) 147-171.
[001] [2] W.-Y. Chang and D.St.P. Richards, Finite-sample inference with monotone incomplete multivariate normal data. I, J. Multivariate Anal. 100 (2009) 1883-1899. doi: 10.1016/j.jmva.2009.05.003.
[002] [3] A.P. Dempster, N.M. Laird and D.B. Rubin, Maximum likelihood from incomplete data via the EM algorithm, J.R. Stat. Soc. Ser. B Stat. Methodol. 39 (1977) 1-38. doi: 10.2307/2984875. | Zbl 0364.62022
[003] [4] T. Kanda and Y. Fujikoshi, Some basic properties of the MLE's for a multivariate normal distribution with monotone missing data, Amer. J. Math. Management. Sci. 18 (1998) 161-190. doi: 10.1080/01966324.1998.10737458. | Zbl 0919.62052
[004] [5] K. Koizumi and T. Seo, Testing equality of two mean vectors and simultaneous confidence intervals in repeated measures with missing data, J. Japanese Soc. Comput. Statist. 22 (2009) 33-41. doi: 10.5183/jjscs.22.1_33. | Zbl 1261.62012
[005] [6] K. Koizumi and T. Seo, Simultaneous confidence intervals among k mean vectors in repeated measures with missing data, Amer. J. Math. Management Sci. 29 (2009) 263-275. | Zbl 1191.62126
[006] [7] Y. Maruyama, Asymptotic expansions of the null distributions of some test statistics for profile analysis in general distributions, J. Statist. Plann. Inference 137 (2007) 506-526. doi: 10.1016/j.jspi.2006.01.010. | Zbl 1102.62015
[007] [8] D.F. Morrison, Multivariate Statistical Methods, 4th ed (Duxbury, 2005). | Zbl 0183.20605
[008] [9] N. Okamoto, N. Miura and T. Seo, On the distributions of some test statistics for profile analysis in elliptical populations, Amer. J. Math. Management Sci. 26 (2006) 1-31. | Zbl 1154.62344
[009] [10] N. Seko, A. Yamazaki and T. Seo, Tests for mean vector and simultaneous confidence intervals with two-step monotone missing data, SUT J. Math. 48 (2012) 13-36. | Zbl 06187558
[010] [11] T. Seo and M.S. Srivastava, Testing equality of means and simultaneous confidence intervals in repeated measures with missing data, Biom. J. 42 (2000) 981-993. doi: 10.1002/1521-4036(200012)42:8<981::AID-BIMJ981>3.0.CO;2-O. | Zbl 0960.62026
[011] [12] N. Shutoh, M. Kusumi, W. Morinaga, S. Yamada and T. Seo, Testing equality of mean vectors in two sample problem with missing data, Comm. Statist. Simulation Comput. 39 (2010) 487-500. doi: 10.1080/03610910903480842. | Zbl 1192.62155
[012] [13] N. Shutoh, M. Hyodo and T. Seo, An asymptotic approximation for EPMC in linear discriminant analysis based on two-step monotone missing samples, J. Multivariate Anal. 102 (2011) 252-263. doi: 10.1016/j.jmva.2010.09.002. | Zbl 1327.62381
[013] [14] M.S. Srivastava, Multivariate data with missing observations, Comm. Statist. Theory Methods 14 (1985) 775-792. doi: 10.1080/03610928508828949. | Zbl 0578.62054
[014] [15] M.S. Srivastava and E.M. Carter, The maximum likelihood method for non-response in sample survey, Survey Methodology 12 (1986) 61-72.
[015] [16] M.S. Srivastava, Profile analysis of several groups, Comm. Statist. Theory Methods 16 (1987) 909-926. doi: 10.1080/03610928708829411. | Zbl 0634.62059