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On a weighted bootstrap approximation of the Lp norms of kernel density estimators

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  • Liu, Bo
  • Mojirsheibani, Majid

Abstract

A weighted bootstrap method is considered to approximate the distribution of the Lp norms of kernel density estimates. Here p is any number in [1,∞). Using a Komlós–Major–Tusnády type approximation (Komlós et al., 1975) for weighted bootstrap processes, due to Horváth et al. (2000), we establish unconditional bootstrap central limit theorems for these Lp statistics.

Suggested Citation

  • Liu, Bo & Mojirsheibani, Majid, 2015. "On a weighted bootstrap approximation of the Lp norms of kernel density estimators," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 65-73.
    • Handle: RePEc:eee:stapro:v:105:y:2015:i:c:p:65-73
    DOI: 10.1016/j.spl.2015.06.005
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    References listed on IDEAS

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    1. Burke, Murray D., 2000. "Multivariate tests-of-fit and uniform confidence bands using a weighted bootstrap," Statistics & Probability Letters, Elsevier, vol. 46(1), pages 13-20, January.
    2. Horváth, Lajos & Kokoszka, Piotr & Steinebach, Josef, 2000. "Approximations for weighted bootstrap processes with an application," Statistics & Probability Letters, Elsevier, vol. 48(1), pages 59-70, May.
    3. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
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