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B0369
Title: On the performance of weighted bootstrapped kernel deconvolution density estimators Authors:  William Pouliot - University of Birmingham (United Kingdom) [presenting]
Abstract: A weighted bootstrap approach is proposed which can improve on current methods to approximate the finite sample distribution of normalized maximal deviations of the kernel density estimators in the case of {\it ordinary smooth} errors. Using results from the approximation theory for weighted bootstrap empirical processes, we establish an unconditional weak limit theorem for the corresponding weighted bootstrap statistics. Because the proposed method uses weights that are not necessarily confined to be uniform (as in Efron's original bootstrap), it provides the practitioner with additional flexibility for choosing the weights. As in immediate consequence of our results, one can construct uniform confidence bands, or perform goodness-of-fit tests, for the underlying density. We have also carried out some numerical examples which show that, depending on the bootstrap weights chosen, the proposed methods has the potential to perform better than the current procedures in the literature.