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Local Quadratic Regression: Maximizing Performance via a Modified PRESS** for Bandwidths Selection

Year: 2023       Vol.: 72       No.: 1      

Authors: E. Edionwe and O. Eguasa


In the application of nonparametric regression model, it is a well-established fact that the bandwidth - also called smoothing parameter- is the single most crucial parameter that determines the quality of the estimated responses that are obtained from the regression procedure, and that its choice (how small or large the size) is hugely influenced by the criterion that is applied for its selection. Under small-sample settings, which is typical of response surface studies, the penalized Prediction Error Sum of Squares (PRESS**) criterion is recommended for selecting this all-important parameter. However, for the purpose of selecting bandwidths of improved statistical properties, we propose a modified version of the PRESS** criterion specifically for Local Quadratic Regression (LQR) model. Results from simulated data as well as those from two popular problems from the literature show that LQR procedure that utilizes the bandwidths selected via the proposed modified criterion performs outstandingly better than its counterpart that utilizes bandwidths selected via PRESS** criterion.

Keywords: Desirability Function, Hat matrix, Penalized Prediction Error Sum of Squares, Response Surface Methodology

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