Project/Area Number  10680320 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
Research Field 
Statistical science

Research Institution  Keio University 
Principal Investigator 
SHIMIZU Kunio Keio University, Department of Mathematics, Professor, 理工学部, 教授 (60110946)

CoInvestigator(Kenkyūbuntansha) 
MINAMI Mihoko The Institute of Statistical Mathematics, Associate Professor, 文部省・統計数理研究所, 助教授 (70277268)
MIYAOKA Etsuo Science University of Tokyo, Department of Mathematics, Associate Professor, 理学部・2部, 助教授 (70200128)
TAKAGIWA Mutsumi Keio University, Department of Mathematics, Instructor, 理工学部, 助手 (30306849)

Project Fiscal Year 
1998 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥2,000,000 (Direct Cost : ¥2,000,000)
Fiscal Year 1999 : ¥700,000 (Direct Cost : ¥700,000)
Fiscal Year 1998 : ¥1,300,000 (Direct Cost : ¥1,300,000)

Keywords  Missing data / Maximum likelihood estimation / Restricted maximum likelihood estimation / Threshold method / Distribution of rainfall / Distribution of cloudbase height / 欠測データ / 最尤推定 / 制限付き最尤推定 / しきい値法 / 降雨量分布 / 雲底分布 / 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 
Research Abstract 
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 rainrate first product moment and covariance were proposed
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(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 rainfall 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 plugin 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 plugin estimate by the REML estimation tends to have smaller mean square error than that by the ML estimation. (4) The groundbased lidar data (June 1996March 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 groundbased lidar measurement, clouds above thick lower clouds are not detected. The cloud overlapping model will be validated by combining the statistical analysis of groundbased lidars and the space lidar. (5) Other are in Miyaoka and Tazaki (1999) and in Smith and Miyaoka (1999). Less
