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Revisiting Akaike’s final prediction error and the Generalized Cross Validation Criteria in Regression from the Same Perspective: From Least Squares to Ridge Regression and Smoothing Splines

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Open Journal of Statistics 2023年第5期13卷 694-716页

作者： Jean Raphael Ndzinga Mvondo Eugène-Patrice Ndong Nguéma Department of Mathematics Ecole Polytechnique Yaoundé I Cameroon

In regression, despite being both aimed at estimating the Mean Squared prediction error (MSPE), Akaike’s final prediction error (FPE) and the Generalized Cross Validation (GCV) selection criteria are usually derived from two quite different perspectives. Here, settling on the most commonly accepted definition of the MSPE as the expectation of the squared prediction error loss, we provide theoretical expressions for it, valid for any linear model (LM) fitter, be it under random or non random designs. Specializing these MSPE expressions for each of them, we are able to derive closed formulas of the MSPE for some of the most popular LM fitters: Ordinary Least Squares (OLS), with or without a full column rank design matrix;Ordinary and Generalized Ridge regression, the latter embedding smoothing splines fitting. For each of these LM fitters, we then deduce a computable estimate of the MSPE which turns out to coincide with Akaike’s FPE. Using a slight variation, we similarly get a class of MSPE estimates coinciding with the classical GCV formula for those same LM fitters.

关键词： Linear Model Mean Squared prediction error final prediction error Generalized Cross Validation Least Squares Ridge Regression

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Jackknife Model Averaging for Quantile Single-Index Coefficient Model

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Journal of Systems Science & Complexity 2024年第4期37卷 1685-1713页

作者： SUN Xianwen ZHANG Lixin School of Mathematical Sciences Zhejiang UniversityHangzhou 310058China School of Statistics and Mathematics Zhejiang Gongshang UniversityHangzhou 310018China

In the past two decades,model averaging,as a way to solve model uncertainty,has attracted more and more *** this paper,the authors propose a jackknife model averaging(JMA) method for the quantile single-index coefficient model,which is widely used in *** model misspecification,the model averaging estimator is proved to be asymptotically optimal in terms of minimizing out-of-sample quantile *** experiments are conducted to compare the JMA method with several model selections and model averaging methods,and the results show that the proposed method has a satisfactory *** method is also applied to a real dataset.

关键词： final prediction error JMA criterion model averaging quantile loss single-index coefficient model

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