Smoothing for small samples with model misspecification: Nonparametric and semiparametric concerns

James Mays and Jeffrey Birch

Journal of Applied Statistics, 2002, vol. 29, issue 7, 1023-1045

Abstract: Our goal is to find a regression technique that can be used in a small-sample situation with possible model misspecification. The development of a new bandwidth selector allows nonparametric regression (in conjunction with least squares) to be used in this small-sample problem, where nonparametric procedures have previously proven to be inadequate. Considered here are two new semiparametric (model-robust) regression techniques that combine parametric and nonparametric techniques when there is partial information present about the underlying model. A general overview is given of how typical concerns for bandwidth selection in nonparametric regression extend to the model-robust procedures. A new penalized PRESS criterion (with a graphical selection strategy for applications) is developed that overcomes these concerns and is able to maintain the beneficial mean squared error properties of the new model-robust methods. It is shown that this new selector outperforms standard and recently improved bandwidth selectors. Comparisons of the selectors are made via numerous generated data examples and a small simulation study.

Date: 2002
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DOI: 10.1080/0266476022000006720

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