Article (Scientific journals)
Parametric Stein operators and variance bounds
LEY, Christophe; Swan, Yvik
2016In Brazilian Journal of Probability and Statistics, 30 (2), p. 171 - 195
Peer reviewed
 

Files


Full Text
14-BJPS271.pdf
Author postprint (269.3 kB)
Download

All documents in ORBilu are protected by a user license.

Send to



Details



Keywords :
Chernoff inequality; Cramér–Rao inequality; Parameter of interest; Stein characterization; Stein’s method; Statistics and Probability
Abstract :
[en] Stein operators are (differential/difference) operators which arise within the so-called Stein’s method for stochastic approximation.We propose a new mechanism for constructing such operators for arbitrary (continuous or discrete) parametric distributions with continuous dependence on the parameter. We provide explicit general expressions for location, scale and skewness families. We also provide a general expression for discrete distributions. We use properties of our operators to provide upper and lower variance bounds (only lower bounds in the discrete case) on functionals h(X) of random variables X following parametric distributions. These bounds are expressed in terms of the first two moments of the derivatives (or differences) of h. We provide general variance bounds for location, scale and skewness families and apply our bounds to specific examples (namely the Gaussian, exponential, gamma and Poisson distributions). The results obtained via our techniques are systematically competitive with, and sometimes improve on, the best bounds available in the literature.
Disciplines :
Mathematics
Author, co-author :
LEY, Christophe ;  University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) ; Département de Mathématique, Université libre de Bruxelles, Brussels, Belgium
Swan, Yvik;  Département de Mathématique, Université de Liège, Liège, Belgium
External co-authors :
yes
Language :
English
Title :
Parametric Stein operators and variance bounds
Publication date :
May 2016
Journal title :
Brazilian Journal of Probability and Statistics
ISSN :
0103-0752
Publisher :
Brazilian Statistical Association
Volume :
30
Issue :
2
Pages :
171 - 195
Peer reviewed :
Peer reviewed
Available on ORBilu :
since 25 November 2023

Statistics


Number of views
13 (1 by Unilu)
Number of downloads
4 (0 by Unilu)

Scopus citations®
 
11
Scopus citations®
without self-citations
3
OpenCitations
 
10
OpenAlex citations
 
21
WoS citations
 
10

publications
19
supporting
0
mentioning
22
contrasting
0
Smart Citations
19
0
22
0
Citing PublicationsSupportingMentioningContrasting
View Citations

See how this article has been cited at scite.ai

scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.

Bibliography


Similar publications



Sorry the service is unavailable at the moment. Please try again later.
Contact ORBilu