Relative Rates of Convergence for Efficient Model Selection Criteria in Linear Regression
研究了在参数模型（使用AIC选择参数个数）与非参数平滑（使用交叉验证选择平滑参数）两种方法中，所选估计量的均方积分误差相对于最优估计量的收敛速度，并证明了AIC在参数情形下可达到任意正ξ的op(n^{-1/2+ξ})速度。
Two approaches to estimating a smooth regression function not specified by a finite number of parameters are (i) to fit a parametric model to the data, with the number of parameters selected by the Akaike information criterion, AIC, and (ii) to use nonparametric smoothing techniques, with the smoothing parameter selected by cross-validation or some other automatic method. We consider the relative rate of convergence of the mean integrated squared error of the selected estimator compared to the best possible estimator in the class of candidates under consideration. We extend results of Shibata (1981) to show that the relative rate of convergence using AIC in the parametric case can be as fast as op(n−½+ξ) for arbitrary positive ξ. We also show that this rate can be attained in the special cases of polynomial and trigonometric regression.