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岭回归系数的若干代数性质AI 解读

Summary This note is concerned with one parameter ridge estimators in a multiple linear regression context as described by Hoerl and Kennard (Technometrics, 12 (1970), pp. 55-68). These estimators are rational functions of the ridge parameter, and some properties concerning sign changes and asymptotic behaviour are noted. Further properties of these estimators are derived assuming that the x'x matrix possesses intraclass (or uniform) correlation structure. Some of these…

若干岭型估计量的蒙特卡洛评估AI 解读

Consider the standard linear model . Ridge regression, as viewed here, defines a class of estimators of indexed by a scalar parameter k. Two analytic methods of specifying k are proposed and evaluated in terms of mean square error by Monte Carlo simulations. With three explanatory variables and determined by the largest eigenvalue of the correlation matrix, least squares is dominated by these estimators in all cases investigated; however, mixed results are obtained with…