Study of semiparametic multiple regression using SIR-PPR algorithm

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The achievement of our study are as follows :1) Based on modified criteria for canonical discriminant analysis, we developed a criterion for selection of edr space using SIR, and examined its performance with Monte-Carlo simulation.(in preparation for submission)2) We developed a new algorithm for SIR using Principal point method, which works well in the cases where data have either symmetric dependence or a distribution which severely violates elliptically symmetric. Simulation study is performed for illustration.(Reported at Symposium on "Statistics, Combinatorics and Related Areas", Bumbai (India), 2000., in preparation for submission)3) In order to avoid over fitting with B-spline smoothing method, we consider other arrangements based on the number of sample points in each interval. We choose knots such that each interval contains about the same number of samples. These knot placement schemes are compared through the Monte Carlo simulation.(Submitted)4) We developed a method to select the better of two types of models : a polynomial with low degree and a B-spline model, using the common information criterion. The methodology can be effectively applied to multiple nonparametric regression analysis.(Submitted)5) We analyzed the relationship between price of detached houses located in the western suburbs of Hiroshima and their environmental conditions such as area of building site, size of building, age of building, degree of commuting convenience of the site, distance from city center using nonparametric regression model.(J.of the Faculty for Human Development, Hiroshima Jogakuin Univ. 7,57-65,2000)6) We analyzed municipality-specific SMR of lung cancer during 1975-1994 in Japan using nonparametric regression, and found that SMR was high at or near the coastline irrespective of the direction of the nearest coastline..(Jpn J Clinical Oncology, 30,557-561,2000)