Estimation of parametric functions for multivariate normal distributions with incomplete observations

完全样本多元正态分布的统计推断理论在许多多元分析教科书中都可以看到。一些专著论述了当给出不完整或遗漏的观察时的情况。在本研究中，我们主要研究具有不完全观测的多元正态分布的统计估计。主要研究结果如下：(1)生态位重叠度被用来评价两个种群的相似性。在完全样本的情况下，考虑了均值和协方差矩阵未知的多元正态分布样本的松田测度估计问题(Minami和Shimizu，1999)。推导了松下测度估计的渐近方差和偏差，并比较了三种减少偏差的方法。提出了基于…的面雨率、一次积矩和协方差阈值估计方法More(Hossain和Shimizu，1999)。实证研究表明，对于东京都的降雨资料，第一乘积矩与两个不同地理位置(陆地和岛屿)超过两个阈值的概率之间存在很强的相关性。以二元对数正态分布为模型，通过最小化渐近归一化方差来选择理论上的最优阈值。(3)讨论了当小生境为具有缺失观测值的二元正态分布(Minami、Shimizu和Mishra出现)时的松下测度估计问题，讨论了基于极大似然(ML)估计和离散参数的约束极大似然(REML)估计的松下测度的插件估计问题。仿真研究表明，基于REML估计的插件估计比基于ML估计的估计具有更小的均方误差。(4)分析了日本国立环境研究所紧凑型激光雷达在筑波连续观测的地面激光雷达数据(Takagiwa等，见下文)。研究了它们的垂直分布和季节变化。在地面激光雷达测量中，不能探测到厚厚的低层云上方的云。云重叠模型将通过结合地面激光雷达和空间激光雷达的统计分析来验证。(5)其他是在宫冈和高崎(1999)和在Smith和宫冈(1999)。较少

The theory of statistical inference in multivariate normal distributions with complete samples can be seen in many textbooks of multivariate analysis. Some monographs deal with the case when incomplete or missing observations are given. In this research we mainly studied statistical estimation for multivariate normal distributions with incomplete observations. The following are the main results.(1) Measures of niche overlap are used to asses the similarity of two populations. The problem of estimating Matusita's measure when samples from multivariate normal distributions with unknown mean vectors and covariance matrices was considered for the case of complete samples (Minami and Shimizu, 1999). Asymptotic variances and biases of Matusita's measure estimates were derived and three bias reduction methods were compared. The case for incomplete observations should be studied in the future.(2) Threshold methods for estimating area rain-rate first product moment and covariance were proposed … More (Hossain and Shimizu, 1999). Empirical study shows a strong correlation between the first product moment and the, probability of exceeding two threshold values for two geographically different locations, land and island, for Tokyo Metropolitan rain-fall data. Theoretical optimal thresholds under the bivariate lognormal distribution as a model were chosen by minimizing the asymptotic normalized variance. A good agreement between the empirical and theoretical results was observed.(3) The problem of estimating Matusita's measure when the niches are bivariate normal distributions with missing observations was discussed (Minami, Shimizu and Mishra, to appear).The plug-in estimates of Matusita's measure by the Maximum Likelihood (ML) estimates and the Restricted Maximum Likelihood (REML) estimates for dispersion parameters were considered. Simulation study shows that the plug-in estimate by the REML estimation tends to have smaller mean square error than that by the ML estimation.(4) The ground-based lidar data (June 1996-March 1999) continuously observed in Tsukuba with the National Institute for Environmental Studies compact lidar were analyzed (Takagiwa, et al., to appear). The vertical distribution and seasonal variation were studied. In the ground-based lidar measurement, clouds above thick lower clouds are not detected. The cloud overlapping model will be validated by combining the statistical analysis of ground-based lidars and the space lidar.(5) Other are in Miyaoka and Tazaki (1999) and in Smith and Miyaoka (1999). Less