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

Mizuki Onozawa; Sho Takahashi; Takashi Seo

Discussiones Mathematicae Probability and Statistics (2013)

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

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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