Development of Some Multivariate Statistical Inference Procedures for Missing and High Dimensional Data and Its Application

当数据中含有缺失观测值时，我们得到了均值向量检验的一些结果。特别地，当数据集具有两步单调缺失数据时，我们给出了单样本和双样本均值向量的似然比检验统计量和Hotelling型检验统计量的检验方法.我们还给出了任何和所有线性化合物的平均值的同时置信区间。此外，通过蒙特卡罗模拟研究了该近似的准确性。考虑了两步单调缺失数据下均值向量和协方差阵的给定值的检验问题，给出了似然比检验统计量和一些结果。对于高维数据的研究，我们在判别分析和多元正态性检验等问题上得到了一些结果。

We obtained some results for the tests of mean vectors when the data have missing observations. In particular, we gave the test procedures for mean vectors using the likelihood ratio test statistic and Hotelling type test statistic for the one sample and two sample problems when the data set has two-step monotone missing data. We also gave the simultaneous confidence intervals for any and all linear compounds of the mean. Further, the accuracy of the approximation is investigated by Monte Carlo simulation. Testing specified values for the mean vector and the covariance matrix with a two-step monotone missing data were considered and derived the likelihood ratio test statistic and some results. As for the study of high dimensional data, we obtained some results for the problem of discriminant analysis and testing for multivariate normality and so on.