文章基本信息

标题：Central limit theorems for the $L_{p}$-error of smooth isotonic estimators
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作者：Hendrik P. Lopuhaä ; Eni Musta
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2019
卷号：13
期号：1
页码：1031-1098
DOI：10.1214/19-EJS1550
语种：English
出版社：Institute of Mathematical Statistics
摘要：We investigate the asymptotic behavior of the $L_{p}$-distance between a monotone function on a compact interval and a smooth estimator of this function. Our main result is a central limit theorem for the $L_{p}$-error of smooth isotonic estimators obtained by smoothing a Grenander-type estimator or isotonizing the ordinary kernel estimator. As a preliminary result we establish a similar result for ordinary kernel estimators. Our results are obtained in a general setting, which includes estimation of a monotone density, regression function and hazard rate. We also perform a simulation study for testing monotonicity on the basis of the $L_{2}$-distance between the kernel estimator and the smoothed Grenander-type estimator.