Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/78420
Title: Moderate deviations and nonparametric inference for monotone functions
Authors: Gao, FQ
Xiong, J
Zhao, XQ 
Keywords: Grenander estimator
Interval censored data
Large deviations
Moderate deviations
Nonparametric MLE
Self-normalized limit
Strong approximation
Talagrand inequality
Issue Date: 2018
Publisher: Institute of Mathematical Statistics
Source: Annals of statistics, June 2018, v. 46, no. 3, p. 1225-1254 How to cite?
Journal: Annals of statistics 
Abstract: This paper considers self-normalized limits and moderate deviations of nonparametric maximum likelihood estimators for monotone functions. We obtain their self-normalized Cramer-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.
URI: http://hdl.handle.net/10397/78420
ISSN: 0090-5364
DOI: 10.1214/17-AOS1583
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