Page 273 - Contributed Paper Session (CPS) - Volume 7

CPS2099 Takatsugu Yoshioka et al.
Tests for mean vector using approximate degrees
of freedom with two-step monotone missing
data
Tamae Kawasaki, Takashi Seo
Tokyo University of Science, Tokyo, Japan

Abstract
In this study, we consider testing for the mean vector with two-step monotone
missing data. Many statistical methods have been developed to analyse data
with missing values. Additionally, the monotone missing data have been
widely studied in the past. Kawasaki and Seo (2016) derived the asymptotic
expansion of the Hotelling’s type test statistics for the case where the sample
size is large with two-step monotone missing data. The asymptotic first two
moments are obtained using stochastic expansion. The goal of our research is
to propose approximate solutions, which are simpler and better convenience
than previous studies. We approximate the distribution for the Hotelling’s T2
type test statistics by constant times an F distribution by adjusting the degrees
of freedom. The method of adjusting the degrees of freedom are estimated
unknown parameters of degrees of freedoms of the F distribution using the
asymptotic expansion of the Hotelling’s T2 type test statistic by Kawasaki and
Seo (2016). The accuracy of the approximation is investigated using Monte
Carlo simulation.

Keywords
asymptotic expansion; F approximation; missing data; multivariate normal

1. Introduction
In almost all statistical analyses, missing data is a constantly occurring
problem. In this study, we consider the problem of testing for normal mean
vectors when the data set has two-step monotone missing observations.
Let be distributed as the multivariate normal

and be distributed as the multivariate normal
, where

and two-step monotone missing data are drawn from a multivariate normal
population of the form

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