Statistical modelling to treat data with missing value

本研究的目的是建立有效的统计模型，并针对不完全信息（如包含缺失值的数据）的统计推断中估计误差的有效估计方法。将观测信息矩阵和Bootstrap方法得到的方差估计与em -算法得到的泊松混合模型的方差估计进行了比较。Kikuchi和Nomakuchi在日本计算统计学会第17次会议上发表了这一结果（2003.05）。研究了用em -算法对正态混合模型和隐马尔可夫正态模型的参数进行估计，并利用观测到的信息矩阵对估计的方差进行估计。Kikuchi和Nomakuchi将在日本计算统计学会第20次会议上发表这一结果（2006.06）。菊地自2003年起成为厚生劳动省研究项目的研究参与者。我们增加了一个与em算法在临床试验中的应用相关的新主题。我们发展了假设伽玛-威布尔分布和广义伽玛分布的生存函数估计方法。Kikuchi和Nomakuchi在日本计算统计学会第18届会议（2004.05）上发表了这一结果，Kikuchi、Nomakuchi和Anraku在上述研究项目的论文集中发表了题为《EM-algorithm of survival function by EM-algorithm （in Japanese）》的论文。

The purpose of this research was to construct the effective statistical models and to develop the effective method of estimation about the error of the estimates in statistical inference based on incomplete information such as data containing the missing value.We compared the estimates of the variance obtained by the observed information matrix and Bootstrap method for the estimates obtained by EM-algorithm for Poisson mixture model. Kikuchi and Nomakuchi presented this result at the 17th meeting of Japanese Society of Computational Statistics (2003.05).We studied about the estimation of the parameters for normal mixture model and hidden Markov normal model by EM-algorithm and the variance of the estimates by the observed information matrix. Kikuchi and Nomakuchi will present this result at the 20th meeting of Japanese Society of Computational Statistics (2006.06).Kikuchi became the research partaker of the research project of Ministry of Health, Labour and Welfare since 2003. We added a new theme relevant to the application of EM-algorithm to the clinical trial. We developed the method of the estimation of the survival function assuming the Gamma-Weibull distribution and the generalized Gamma distribution. Kikuchi and Nomakuchi presented this result at the 18th meeting of Japanese Society of Computational Statistics (2004.05), and Kikuchi, Nomakuchi and Anraku presented a paper about this result entitled "Estimation of the survival function by EM-algorithm (in Japanese)" on the collected papers of the above research project.