Central limit theorems for the $L_p$-error of smooth isotonic estimators
Statistics Theory
2018-06-01 v1 Statistics Theory
Abstract
We investigate the asymptotic behavior of the -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 -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 -distance between the kernel estimator and the smoothed Grenander-type estimator.
Keywords
Cite
@article{arxiv.1805.12430,
title = {Central limit theorems for the $L_p$-error of smooth isotonic estimators},
author = {Hendrik P. Lopuhaä and Eni Musta},
journal= {arXiv preprint arXiv:1805.12430},
year = {2018}
}