Sequential Data-Adaptive Bandwidth Selection by Cross-Validation for Nonparametric Prediction

Details Sequential Data-Adaptive Bandwidth Selection by Cross-Validation for Nonparametric Prediction Sequential Data-Adaptive Bandwidth Selection by Cross-Validation for Nonparametric Prediction

2010-10-29

arxiv.org/abs/1010.6202v1

Mathematics

Statistics Theory

26 pages

Scientific paper

We consider the problem of bandwidth selection by cross-validation from a sequential point of view in a nonparametric regression model. Having in mind that in applications one often aims at estimation, prediction and change detection simultaneously, we investigate that approach for sequential kernel smoothers in order to base these tasks on a single statistic. We provide uniform weak laws of large numbers and weak consistency results for the cross-validated bandwidth. Extensions to weakly dependent error terms are discussed as well. The errors may be {\alpha}-mixing or L2-near epoch dependent, which guarantees that the uniform convergence of the cross validation sum and the consistency of the cross-validated bandwidth hold true for a large class of time series. The method is illustrated by analyzing photovoltaic data.

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