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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Generalized functional linear model ： ウィキペディア英語版 Generalized functional linear model The generalized functional linear model (GFLM) is an extension of the generalized linear model (GLM) that allows one to regress univariate responses of various types (continuous or discrete) on functional predictors, which are mostly random trajectories generated by a square-integrable stochastic processes. Similarly to GLM, a link function relates the expected value of the response variable to a linear predictor, which in case of GFLM is obtained by forming the scalar product of the random predictor function $X$ with a smooth parameter function $\backslash beta$. Functional Linear Regression, Functional Poisson Regression and Functional Binomial Regression, with the important Functional Logistic Regression included, are special cases of GFLM. Applications of GFLM include classification and discrimination of stochastic processes and functional data. ==Overview== A key aspect of GFLM is estimation and inference for the smooth parameter function $\backslash beta$ which is usually obtained by dimension reduction of the infinite dimensional functional predictor. A common method is to expand the predictor function $X$ in an orthonormal basis of L2 space, the Hilbert space of square integrable functions with the simultaneous expansion of the parameter function in the same basis. This representation is then combined with a truncation step to reduce the contribution of the parameter function $\backslash beta$ in the linear predictor to a finite number of regression coefficients. Functional principal component analysis (FPCA) that employs the Karhunen–Loève expansion is a common and parsimonious approach to accomplish this. Other orthogonal expansions, like Fourier expansions and B-spline expansions may also be employed for the dimension reduction step. The Akaike information criterion (AIC) can be used for selecting the number of included components. Minimization of cross-validation prediction errors is another criteria often used in classification applications. Once the dimension of the predictor process has been reduced, the simplified linear predictor allows to use GLM and quasi-likelihood estimation techniques to obtain estimates of the finite dimensional regression coefficients which in turn provide an estimate of the parameter function $\backslash beta$ in the GFLM. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Generalized functional linear model」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.