Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion
本文提出并检验了一种改进的AIC准则（AICC），用于选择非参数回归中的平滑参数，适用于任何线性平滑器，避免了其他经典方法（如GCV或AIC）的过度变异和欠平滑问题。
Many different methods have been proposed to construct nonparametric estimates of a smooth regression function, including local polynomial, (convolution) kernel and smoothing spline estimators. Each of these estimators uses a smoothing parameter to control the amount of smoothing performed on a given data set. In this paper an improved version of a criterion based on the Akaike information criterion (AIC), termed AICC, is derived and examined as a way to choose the smoothing parameter. Unlike plug‐in methods, AICC can be used to choose smoothing parameters for any linear smoother, including local quadratic and smoothing spline estimators. The use of AICC avoids the large variability and tendency to undersmooth (compared with the actual minimizer of average squared error) seen when other ‘classical’ approaches (such as generalized cross‐validation (GCV) or the AIC) are used to choose the smoothing parameter. Monte Carlo simulations demonstrate that the AICC‐based smoothing parameter is competitive with a plug‐in method (assuming that one exists) when the plug‐in method works well but also performs well when the plug‐in approach fails or is unavailable.