Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion

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 give...

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Bibliographic Details
Published in:Journal of the Royal Statistical Society. Series B, Statistical methodology Statistical methodology, 1998, Vol.60 (2), p.271-293
Main Authors: Hurvich, Clifford M., Simonoff, Jeffrey S., Tsai, Chih-Ling
Format: Article
Language:English
Subjects:
Computer simulation
Consistent estimators
Convolution kernel regression estimator
Criteria
Data smoothing
Datasets
Density estimation
Estimation
Estimation methods
Estimators
Linear regression
Local polynomial regression estimator
Mathematical independent variables
Monte Carlo methods
Parameters
Parametric models
Plug-in method
Polynomials
Regression
Regression analysis
Smoothing
Smoothing spline regression estimator
Splines
Statistics
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Summary: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 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.
ISSN:1369-7412
1467-9868
DOI:10.1111/1467-9868.00125