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Title: Bartlett correction of $T^2$ type test statistic with two-step monotone missing data in two-sample problem Authors:  Tamae Kawasaki - Aoyama Gakuin University (Japan) [presenting]
Takashi Seo - Tokyo University of Science (Japan)
Abstract: The problem of testing the equality of mean vectors in a two-sample problem with two-step monotone missing data is discussed. Under the assumption that the population covariance matrices are equal, we derive the stochastic expansion of Hotelling's $T^2$ type statistic for the case where sample sizes are large. The asymptotic first two moments of $T^2$ type statistic are obtained by its stochastic expansion. We also propose the Bartlett corrected statistic for two-step monotone missing data. Finally, the accuracy and asymptotic behavior of the approximation are investigated by Monte Carlo simulation.