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On wavelet projection kernels and the integrated squared error in density estimation

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  • Giné, Evarist
  • Madych, W.R.

Abstract

It is shown that the integrated squared errors of wavelet projection estimators of a density f satisfy both the central limit theorem and the law of the iterated logarithm under the essentially minimal assumption f∈Lp for some p>2 and very mild conditions on the scaling function.

Suggested Citation

  • Giné, Evarist & Madych, W.R., 2014. "On wavelet projection kernels and the integrated squared error in density estimation," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 32-40.
    • Handle: RePEc:eee:stapro:v:91:y:2014:i:c:p:32-40
    DOI: 10.1016/j.spl.2014.03.029
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    References listed on IDEAS

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    1. 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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    Cited by:

    1. Aleksandr Beknazaryan & Hailin Sang & Peter Adamic, 2023. "On the integrated mean squared error of wavelet density estimation for linear processes," Statistical Inference for Stochastic Processes, Springer, vol. 26(2), pages 235-254, July.
    2. Krebs, Johannes T.N., 2018. "Nonparametric density estimation for spatial data with wavelets," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 300-319.

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