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On the performance of weighted bootstrapped kernel deconvolution density estimators. (English) Zbl 1452.62260

Summary: We propose a weighted bootstrap approach that can improve on current methods to approximate the finite sample distribution of normalized maximal deviations of kernel deconvolution density estimators in the case of 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 an 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 method has the potential to perform better than the current procedures in the literature.

MSC:

62G07 Density estimation
62G09 Nonparametric statistical resampling methods
60F05 Central limit and other weak theorems

Software:

decon
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Full Text: DOI Link

References:

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