Keeping the estimator of regression parameters stable and achieving variable selection of the model, we focus on Breiman's non-negative garrote (NNG) as a shrinkage estimator and propose two boosting methods of the NNG. One is the method that NNG runs with multi-fold cross validation in each boosting iterations, and the other is the method that NNG runs without cross validation in each boosting iterations. Then, we evaluated the performance of the proposed methods through small scale simulation. As a result, the proposed methods kept the estimator more stable than the naive NNG. So we have showed boosting method is also useful for the estimation of regression parameters.

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In these years, Japanese media is bringing up a issue of decline in a quality of teachers in the field of education. In this research, we noted that the problem. Ministry of Education, Culture, Sports, Science and Technology has been evaluating teachers about public elementary school, junior high school and high school since 2000. Respondents judge teachers by subjectivity, but if two or more respondents judge similar evaluation, it is assumed the objective evaluation. Therefore, we consolidated that two or more respondents' opinions by using Analytic Hierarchy Process (AHP) and Structural Equation Modeling (SEM). Toyoda et al. (2004) proposed Group AHP by SEM (GAS). In the fields of education, the presumption is difficult by using SEM, because the size of the sample about a questionnaire of a manager and teachers is small. The present study proposes system of cramming school teacher's leadership evaluation by using AHP and SEM.

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There are multiple comparison procedures to identify a minimum effective dose level where the effect on a response first appears with increasing dose level in dose response test. These procedures are used to carry out the test based on the all observations obtained across all dose levels. However, if it is difficult to obtain the observations easily at each dose level or we want an early decision in the test based on few observations, it is meaningful to develop the procedure that identifies sequentially a minimum effective dose level based on the sequentially obtained observations. In this study, we propose a sequential contrast procedure to identify the minimum effective dose level by sequentially investigating the change of the response by using the contrast among population means. In simulation studies, we compare the sequential Dunnett's procedure developed and the sequential contrast procedure in terms of the power of the test. In a case study, we apply these two procedures to the dose response test on workability of mortar in concrete technology.

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PCA (principal component analysis) is a technique for visualizing a continuous data with p(≥3) variables through dimension reduction. As result, the n observations are summarized by k(=2,3,…) principal component scores. The purpose of this article is to develop the method for finding a subset of q(≤p) variables best predicting k principal component scores obtained from all p variables. We propose an algorithm for variable selection method using regression imputation technique for principal component analysis.

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From 1997, I proposed several different kinds of discriminant functions using by mathematical programming in my research. At first, IP-OLDF and LP-OLDF are proposed. IP-OLDF is linear discriminant function based on MMN (Minimum Misclassification Number) criteria. This model is defined on both data and discriminant coefficient spaces. So, new facts about discriminant analysis are obtained: 1) relationship about discriminant coefficients and MMN, 2) MMN decreases monotonously on the models selected by forward stepwise method. 3) Misclassification numbers of different discriminant models are regressed by MMN. And different models are evaluated by these regression lines. But, IP-OLDF needs huge computational power because it uses integer programming. In addition to this, it rarely looks for wrong solution if data isn't in general position. LP-OLDF is derived from IP-OLDF by minor modification of decision variables. This model is one of L_1 norm discriminant model that is very popular in these researches. In 2003, faster algorithm of IP-OLDF is proposed. Firstly, data is analyzed by LP-OLDF. Secondly, classified cases are fixed and IP-OLDF is applied for misclassified cases. This algorism is evaluated by several data and obtained good results. After 2005, Revised IP-OLDF is proposed. This model can find MMN correctly, even though data is not in general position. So, I can evaluate Revised IP-OLDF with other discriminate models, especially SVM. In this research, new algorithm of soft margin maximization SVM is found. This model obtained good result compared with soft margin SVM. Sometimes, it can find MMN.

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