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

我们考虑了带缺失数据的多元统计理论和多元正态检验。特别是，我们关注缺失数据的判别分析。给出了单调缺失数据下方差参数的估计。并利用该估计改进了线性判别函数EPMC的渐近逼近，进而给出了两类高维数据多元正态估计的改进统计量。并利用AIC和Glasso估计提出了高维数据中方差-协方差矩阵的一种新的估计方法。

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.