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2019 Central limit theorems for the $L_{p}$-error of smooth isotonic estimators
Hendrik P. Lopuhaä, Eni Musta
Electron. J. Statist. 13(1): 1031-1098 (2019). DOI: 10.1214/19-EJS1550


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.


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Hendrik P. Lopuhaä. Eni Musta. "Central limit theorems for the $L_{p}$-error of smooth isotonic estimators." Electron. J. Statist. 13 (1) 1031 - 1098, 2019.


Received: 1 July 2018; Published: 2019
First available in Project Euclid: 5 April 2019

zbMATH: 07056146
MathSciNet: MR3935844
Digital Object Identifier: 10.1214/19-EJS1550

Primary: 62G20
Secondary: 62G10


Vol.13 • No. 1 • 2019
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