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The adaptive rate of convergence in a problem of pointwise density estimation

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  • Butucea, Cristina

Abstract

We estimate the common density function of n i.i.d. observations, at a fixed point, over Sobolev classes of functions having regularity [beta]. We prove that the optimal rate of convergence cannot be attained in adaptive estimation, i.e. uniformly over [beta] in some interval Bn. A slower rate is shown to be adaptive.

Suggested Citation

  • Butucea, Cristina, 2000. "The adaptive rate of convergence in a problem of pointwise density estimation," Statistics & Probability Letters, Elsevier, vol. 47(1), pages 85-90, March.
    • Handle: RePEc:eee:stapro:v:47:y:2000:i:1:p:85-90
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    References listed on IDEAS

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    1. Christina Butucea, 1998. "Exact Adaptive Pointwise Estimation on Sobolev Classes of Densities," Working Papers 98-18, Center for Research in Economics and Statistics.
    2. repec:crs:wpaper:9818 is not listed on IDEAS
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    Cited by:

    1. Sakshi Arya & Anuj Abhishek, 2023. "Adaptive Estimation of a Function from its Exponential Radon Transform in Presence of Noise," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1127-1155, August.
    2. Liu, Youming & Wu, Cong, 2019. "Point-wise estimation for anisotropic densities," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 112-125.

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