Bootstrap Bandwidth Selection Using an h‐Dependent Pilot Bandwidth

José E. Chacón, Jesús Montanero and Agustín G. Nogales

Scandinavian Journal of Statistics, 2008, vol. 35, issue 1, 139-157

Abstract: Abstract. The problem of choosing the bandwidth h for kernel density estimation is considered. All the plug‐in‐type bandwidth selection methods require the use of a pilot bandwidth g. The usual way to make an h‐dependent choice of g is by obtaining their asymptotic expressions separately and solving the two equations. In contrast, we obtain the asymptotically optimal value of g for every fixed h, thus making our selection ‘less asymptotic’. Exact error expressions show that some usually assumed hypotheses have to be discarded in the asymptotic study in this case. Two versions of a new bandwidth selector based on this idea are proposed, and their properties are analysed through theoretical results and a simulation study.

Date: 2008
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