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On the performance of weighted bootstrapped kernel deconvolution density estimators

Author

Listed:
  • Ali Al-Sharadqah

    (California State University)

  • Majid Mojirsheibani

    (California State University)

  • William Pouliot

    (University of Birmingham)

Abstract

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.

Suggested Citation

  • Ali Al-Sharadqah & Majid Mojirsheibani & William Pouliot, 2020. "On the performance of weighted bootstrapped kernel deconvolution density estimators," Statistical Papers, Springer, vol. 61(4), pages 1773-1798, August.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:4:d:10.1007_s00362-018-1006-0
    DOI: 10.1007/s00362-018-1006-0
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    1. Mojirsheibani, Majid, 2021. "A note on the performance of bootstrap kernel density estimation with small re-sample sizes," Statistics & Probability Letters, Elsevier, vol. 178(C).

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