# Tests for profile analysis based on two-step monotone missing data

• Volume: 33, Issue: 1-2, page 171-190
• ISSN: 1509-9423

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## Abstract

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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.

## How to cite

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Mizuki Onozawa, Sho Takahashi, and Takashi Seo. "Tests for profile analysis based on two-step monotone missing data." Discussiones Mathematicae Probability and Statistics 33.1-2 (2013): 171-190. <http://eudml.org/doc/270843>.

@article{MizukiOnozawa2013,
abstract = {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.},
author = {Mizuki Onozawa, Sho Takahashi, Takashi Seo},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {Hotelling's T²-type statistic; likelihood ratio; profile analysis; two-step monotone missing data; Hotelling’s -type statistic},
language = {eng},
number = {1-2},
pages = {171-190},
title = {Tests for profile analysis based on two-step monotone missing data},
url = {http://eudml.org/doc/270843},
volume = {33},
year = {2013},
}

TY - JOUR
AU - Mizuki Onozawa
AU - Sho Takahashi
AU - Takashi Seo
TI - Tests for profile analysis based on two-step monotone missing data
JO - Discussiones Mathematicae Probability and Statistics
PY - 2013
VL - 33
IS - 1-2
SP - 171
EP - 190
AB - 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.
LA - eng
KW - Hotelling's T²-type statistic; likelihood ratio; profile analysis; two-step monotone missing data; Hotelling’s -type statistic
UR - http://eudml.org/doc/270843
ER -

## References

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1. [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.
2. [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.
3. [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. Zbl0364.62022
4. [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. Zbl0919.62052
5. [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. Zbl1261.62012
6. [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. Zbl1191.62126
7. [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. Zbl1102.62015
8. [8] D.F. Morrison, Multivariate Statistical Methods, 4th ed (Duxbury, 2005). Zbl0183.20605
9. [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. Zbl1154.62344
10. [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. Zbl06187558
11. [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. Zbl0960.62026
12. [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. Zbl1192.62155
13. [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. Zbl1327.62381
14. [14] M.S. Srivastava, Multivariate data with missing observations, Comm. Statist. Theory Methods 14 (1985) 775-792. doi: 10.1080/03610928508828949. Zbl0578.62054
15. [15] M.S. Srivastava and E.M. Carter, The maximum likelihood method for non-response in sample survey, Survey Methodology 12 (1986) 61-72.
16. [16] M.S. Srivastava, Profile analysis of several groups, Comm. Statist. Theory Methods 16 (1987) 909-926. doi: 10.1080/03610928708829411. Zbl0634.62059

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