A comparison of Several Bandwidth Selection Methods for Local Polynomial Regression
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Local Polynomial, Bandwidth, Kernel Function, Simulation
Abstract
In local polynomial regression, choosing the smoothing parameter (bandwidth) is a crucial issue. A too-large value provides over-smoothing. Conversely, a too-small value gives a wiggly estimate, which results in under-smoothing. However, the proper choice of bandwidth can be considered a careful balance of these principles. In this paper, intensive simulation experiments are carried out using R software to compare the practical performance of several bandwidth selection methods, namely the Cross Validation (CV), Generalized Cross Validation (GCV), and Adaptive (ADP). Within the context of these strategies of selecting the optimal bandwidth(s), four different example-regression models have been used under different sample sizes and kernel functions. Results showed that the GCV bandwidth selection criterion appears to give better (smaller) estimates of MSE when the sample sizes (n) are small with a Gaussian kernel function. However, the ADP bandwidth selection appears to give better (smaller) estimates of MSE when the sample sizes (n) are large with the Triweight l kernel function.
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References
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