論文の公開元へProfile analysis and tests for mean vectors with two-step monotone missing data
概要
In this study, we consider the profile analysis and the tests for the mean vectors when the observations have two-step monotone missing data. We often
encounter the problem of missing data in many practical situations. In this
study, we assume that missing pattern is two-step monotone missing data. In
Chapter 2, we discuss profile analysis for two sample and multi-sample problem
with two-step monotone missing data. This is the content of Onozawa et al.
[12]. Profile analysis is known as statistical method when we are interested in
comparing the profiles of several groups. There are three hypotheses known
as parallelism hypothesis, level hypothesis and flatness hypothesis. In normal
population, the profile analysis for two sample problem have been discussed by
using Hotelling’s T 2 -type statistic (see, e.g., Morrison [10]). And Srivastava [17]
gave a profile analysis of several groups based on the likelihood ratio. For the
assumption of nonnormality, Okamoto et al. [11] discussed profile analysis in
elliptical populations. Further Maruyama [9] obtained asymptotic expansions
of the null distributions of some test statistics for general distributions. On
the other hand, when the missing observations are of the monotone-type, the
test for the equality of means have been discussed by many authors. In one
sample problem, Chang and Richards [3] considered the T 2 -type test statistic
for the mean vector with two-step monotone missing data. Further, Anderson
and Olkin [2] obtained the maximum likelihood estimators (MLEs) of mean
vector and covariance matrix for two-step monotone missing data, and Kanda
and Fujikoshi [6] discussed the distribution of these MLEs and expanded for
K-step monotone missing data. Further, Seko et al. [15] discussed the T 2 -type
test statistic and likelihood ratio test statistic using linear interpolation. In two
sample problem, by the same way as Anderson and Olkin [2], the MLEs have
been obtained (see, e.g., Shutoh et al. [16]). Linear interpolation approximation
for the null distribution of the Hotelling’s T 2 -type test statistic and the likelihood ratio test statistic with two-step monotone missing data were reported by
Seko et al. [14].
The organization of Chapter 2 is as follows. ...
