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Estimation of parametric functions for multivariate normal distributions with incomplete observations

具有不完整观测值的多元正态分布的参数函数估计

基本信息

批准号：
10680320
负责人：
SHIMIZU Kunio
金额：
$ 1.28万
依托单位：
Keio University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 1999
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10680320/
关键词：
Missing data Maximum likelihood estimation Restricted maximum likelihood estimation Threshold method Distribution of rainfall Distribution of cloud-base height 相関係数分散安定化変換偏り修正松下の類似度 Lagrange分布族

项目摘要

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

多元正态分布的统计推断理论在多元分析的许多教科书中都有介绍。一些专著处理的情况下，不完整或缺失的意见。本文主要研究不完全观测下多元正态分布的统计估计问题。以下是主要结果。(1)生态位重叠的措施被用来评估两个群体的相似性。当样本来自具有未知均值向量和协方差矩阵的多元正态分布时，估计Matusita测度的问题被考虑用于完全样本的情况（Minami和Shimizu，1999）。渐近方差和偏差的Matusita的措施估计，推导和三个偏差减少方法进行了比较。今后应研究观测不完整的情况。(2)提出了面积雨率一次积矩和协方差的阈值估计方法 ...更多信息（Hossain和Shimizu，1999年）。实证研究表明，第一产品的时刻和，超过两个阈值的两个地理不同的位置，土地和岛屿，东京都降雨数据的概率之间的强相关性。在二元对数正态分布模型下，通过最小化渐近归一化方差选择理论最优阈值。观察到的经验和理论结果之间的一个很好的协议。(3)讨论了当小生境为具有缺失观测值的二元正态分布时Matusita测度的估计问题（Minami，Shimizu和Mishra等），考虑了离散参数的最大似然（ML）估计和限制最大似然（REML）估计对Matusita测度的插入估计.仿真研究表明，插入估计的REML估计往往有较小的均方误差比ML估计。(4)分析了国家环境研究所紧凑型激光雷达在筑波连续观测的地基激光雷达数据（1996年6月至1999年3月）（Takagiwa等人，出现）。研究了其垂直分布和季节变化。在地面激光雷达测量中，厚的低云层上方的云没有被检测到。结合地面激光雷达和空间激光雷达的统计分析，对云重叠模型进行验证。(5)其他的是Miyaoka和Tazaki（1999）以及Smith和Miyaoka（1999）。少