著者

甘利 俊一 川鍋 元明

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:09172270)

巻号頁・発行日

vol.6, no.2, pp.96-109, 1996

参考文献数

19

被引用文献数

10

---

The present paper studies estimation of the coefficient θ of a linear dependence relation y=θx between two variables x and y from n pairs (y_i, x_i), i=1, …, n, of noise-contaminated observations. This is an old problem where the maximum likelihood estimator or the least square estimator is known not to be a,symptotically optimal. A simple estimator which improves the above one is explicitly given. This is a typical example of semiparametric statistical estimation. The method of estimating functions is used to solve the problem. Information geometry is used for elucidating the set of all the estimating functions and the asymptotic efficiency of the related estimators. A fibre structure is composed on the manifold of a semiparametric model and a dual couple of parallel transports are introduced on the fibres.