Asymptotically efficient estimation of the sparsity function at a point

A. H. Welsh

doi:10.1016/0167-7152(88)90103-4

Asymptotically efficient estimation of the sparsity function at a point

A. H. Welsh^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

19 Citations (Scopus)

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.

Original language	English
Pages (from-to)	427-432
Number of pages	6
Journal	Statistics and Probability Letters
Volume	6
Issue number	6
DOIs	https://doi.org/10.1016/0167-7152(88)90103-4
Publication status	Published - May 1988
Externally published	Yes

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10.1016/0167-7152(88)90103-4

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title = "Asymptotically efficient estimation of the sparsity function at a point",

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.",

keywords = "efficient estimation, kernel, mean squared error, order statistics, sparsity function, weak convergence",

author = "Welsh, {A. H.}",

year = "1988",

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T1 - Asymptotically efficient estimation of the sparsity function at a point

AU - Welsh, A. H.

PY - 1988/5

Y1 - 1988/5

N2 - 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.

AB - 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.

KW - efficient estimation

KW - kernel

KW - mean squared error

KW - order statistics

KW - sparsity function

KW - weak convergence

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DO - 10.1016/0167-7152(88)90103-4

M3 - Article

AN - SCOPUS:38249031035

SN - 0167-7152

VL - 6

SP - 427

EP - 432

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 6

ER -

Asymptotically efficient estimation of the sparsity function at a point

Abstract

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