Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/78420
PIRA download icon_1.1View/Download Full Text
Title: Moderate deviations and nonparametric inference for monotone functions
Authors: Gao, F
Xiong, J
Zhao, X 
Issue Date: Jun-2018
Source: Annals of statistics, June 2018, v. 46, no. 3, p. 1225-1254
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.
Keywords: Grenander estimator
Interval censored data
Large deviations
Moderate deviations
Nonparametric MLE
Self-normalized limit
Strong approximation
Talagrand inequality
Publisher: Institute of Mathematical Statistics
Journal: Annals of statistics 
ISSN: 0090-5364
DOI: 10.1214/17-AOS1583
Rights: © Institute of Mathematical Statistics, 2018
The following publication Gao, F., Xiong, J., & Zhao, X. (2018). Moderate deviations and nonparametric inference for monotone functions. The Annals of Statistics, 46(3), 1225-1254 is available at https://dx.doi.org/10.1214/17-AOS1583
Appears in Collections:Journal/Magazine Article

Files in This Item:
File Description SizeFormat 
17-AOS1583.pdf291.57 kBAdobe PDFView/Open
Open Access Information
Status open access
File Version Version of Record
Access
View full-text via PolyU eLinks SFX Query
Show full item record

Page views

95
Last Week
0
Last month
Citations as of Mar 24, 2024

Downloads

19
Citations as of Mar 24, 2024

SCOPUSTM   
Citations

13
Citations as of Mar 22, 2024

WEB OF SCIENCETM
Citations

10
Last Week
0
Last month
Citations as of Mar 28, 2024

Google ScholarTM

Check

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.