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Asymptotically efficient estimation of the sparsity function at a point

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  • Welsh, A. H.

Abstract

The sparsity function is important in nonparametric inference based on order statistics. In this paper, we consider kernel estimation of the sparsity function. We establish an invariance principle for the kernel estimator and then construct a simple adaptive estimator which we show is asymptotically efficient in the mean squared error sense.

Suggested Citation

  • Welsh, A. H., 1988. "Asymptotically efficient estimation of the sparsity function at a point," Statistics & Probability Letters, Elsevier, vol. 6(6), pages 427-432, May.
    • Handle: RePEc:eee:stapro:v:6:y:1988:i:6:p:427-432
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    Cited by:

    1. Pasha Andreyanov & Grigory Franguridi, 2021. "Nonparametric inference on counterfactuals in first-price auctions," Papers 2106.13856, arXiv.org, revised Oct 2024.
    2. Yao Luo & Yuanyuan Wan, 2018. "Integrated-Quantile-Based Estimation for First-Price Auction Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(1), pages 173-180, January.
    3. Wei, Ying & Carroll, Raymond J., 2009. "Quantile Regression With Measurement Error," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1129-1143.
    4. Dilanka S. Dedduwakumara & Luke A. Prendergast & Robert G. Staudte, 2021. "Some confidence intervals and insights for the proportion below the relative poverty line," SN Business & Economics, Springer, vol. 1(10), pages 1-22, October.
    5. Hao Cheng & Ying Wei, 2018. "A fast imputation algorithm in quantile regression," Computational Statistics, Springer, vol. 33(4), pages 1589-1603, December.

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