Central limit theorems for the L_p-error of smooth isotonic estimators

2018/05/31 by Hendrik P. Lopuhaä, Lopuhaä, Hendrik P., Eni Musta +1
Mathematics · #FOS: Mathematics #Statistics Theory (math.ST) #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1805.12430

arxiv created 2018/05/31 · arxiv updated 2018/06/01

Abstract

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 L₂-distance between the kernel estimator and the smoothed Grenander-type estimator.

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