Basic theory and applications for the problem of variable selection in multivariate analysis

本项目的目的是研究各种模型的变量选择问题及相关问题，并将其应用于实际数据。得到的主要结果如下：(1)推广的增长曲线模型参数矩阵的一般线性假设的似然比检验(Fujikoshi et al.(2)导出了高维情形下Wilks‘s Lambda统计量的Edgeworth展开(Wakaki(2006))。(3)发展了图像分类方法(Nishii et al.(4)导出了AIC的渐近分布(Yanagihara等人)。(5)提出了回归模型中变量选择的预测误差准则(Fujikoshi et al.(6)导出了一种贝叶斯信息准则，并将其应用于径向基函数网络模型中平滑参数的选择(Konishi等人)。(7)提出了一种基于连通邻域的聚类方法(Satoh et al.(8)提出了一种基于正态混合模型的单核苷酸多态基因分型方法(Satoh et al.(9)发展了光滑函数统计背景下的一般偏差减少技术，并提出了模型评估和选择问题的准则(Konishi等人)。(10)提出了生长曲线模型的一些模型选择准则(Fujikoshi(2003))。(11)提出了Logistic回归模型中AIC的偏差校正方法(Yanagihara等人)。(12)提出了一种选择B-Spline和多项式回归的方法(Satoh et al.(2003))。

The purpose of this project is to study variable selection problems for various models and related problems, and to apply to the actual data. Main results obtained are as follows.(1) The likelihood ratio tests on a general linear hypothesis of the parameter matrix for an extended growth curve models (Fujikoshi et al. (2006)).(2) Edgeworth expansion of Wilks's lambda statistic is derived for high dimensional case (Wakaki (2006)).(3) Image classification methods are developed (Nishii et al. (2006)).(4) An asymptotic distribution of the AIC is derived (Yanagihara et al. (2005)).(5) Prediction error criterion for selecting of varaibles in regression model is proposed (Fujikoshi et al. (2005)).(6) A Bayesian information criterion is derived and applied to choice of smoothing parameters in radial basis function network models (Konishi et al. (2004)).(7) A clustering method by connected neighborhoods is proposed (Satoh et al. (2004)).(8) A classification method for genotyping of Single nucleotide polymorphisms based on normal mixture model are proposed (Satoh et al. (2004)).(9) A general bias reduction technique in the context of smooth functional statistics is develped and an criterion in model evaluation and selection problems is proposed (Konishi et al. (2003)).(10) Some model selection criteria for grouth curve model are proposed (Fujikoshi (2003)).(11) A bias correction method for AIC in logistic regression models is proposed (Yanagihara et al. (2003)).(12) A method to select B-Spline and Polynomial regression is proposed (Satoh et al. (2003)).