Research on statistical theory in non-regular multi-dimensional data

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We consider the multivariate statistical theory with missing data and the multivariate normality test. In particular we focus on discriminant analysis with missing data. We derive an estimator of variance parameter with monotone missing data. And by using this estimator, we improve the asymptotic approximation for the EPMC of linear discriminant function.Further, we give two types of improved statistic for assessing multivariate normality in high-dimensional data. And we propose a new estimator for variance-covariance matrix in high-dimensional data by using AIC and gLasso estimator.