Open Access
June 2018 Moderate deviations and nonparametric inference for monotone functions
Fuqing Gao, Jie Xiong, Xingqiu Zhao
Ann. Statist. 46(3): 1225-1254 (June 2018). DOI: 10.1214/17-AOS1583

Abstract

This paper considers self-normalized limits and moderate deviations of nonparametric maximum likelihood estimators for monotone functions. We obtain their self-normalized Cramér-type moderate deviations and limit distribution theorems for the nonparametric maximum likelihood estimator in the current status model and the Grenander-type estimator. As applications of the results, we present a new procedure to construct asymptotical confidence intervals and asymptotical rejection regions of hypothesis testing for monotone functions. The theoretical results can guarantee that the new test has the probability of type II error tending to 0 exponentially. Simulation studies also show that the new nonparametric test works well for the most commonly used parametric survival functions such as exponential and Weibull survival distributions.

Citation

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Fuqing Gao. Jie Xiong. Xingqiu Zhao. "Moderate deviations and nonparametric inference for monotone functions." Ann. Statist. 46 (3) 1225 - 1254, June 2018. https://doi.org/10.1214/17-AOS1583

Information

Received: 1 September 2016; Revised: 1 March 2017; Published: June 2018
First available in Project Euclid: 3 May 2018

zbMATH: 06897928
MathSciNet: MR3798002
Digital Object Identifier: 10.1214/17-AOS1583

Subjects:
Primary: 60F10 , 62G20
Secondary: 62G07

Keywords: Grenander estimator , interval censored data , large deviations , Moderate deviations , nonparametric MLE , self-normalized limit , strong approximation , Talagrand inequality

Rights: Copyright © 2018 Institute of Mathematical Statistics

Vol.46 • No. 3 • June 2018
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