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, 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 | Size | Format | |
---|---|---|---|---|
17-AOS1583.pdf | 291.57 kB | Adobe PDF | View/Open |
Page views
111
Last Week
0
0
Last month
Citations as of Sep 22, 2024
Downloads
25
Citations as of Sep 22, 2024
SCOPUSTM
Citations
13
Citations as of Aug 15, 2024
WEB OF SCIENCETM
Citations
10
Last Week
0
0
Last month
Citations as of Sep 26, 2024
Google ScholarTM
Check
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.