Generalized moment estimators based on Stein identities
Publication date
2024-06-17
Document type
Forschungsartikel
Author
Organisational unit
Publisher
Springer Nature
Series or journal
Journal of Statistical Theory and Applications
ISSN
Periodical volume
23
Periodical issue
3
First page
240
Last page
274
Is referenced by
Peer-reviewed
✅
Part of the university bibliography
✅
Language
English
Keyword
Asymptotic distribution
Method of moments
Parametric distributions
Stein identity
Abstract
For parameter estimation of continuous and discrete distributions, we propose a generalization of the method of moments (MM), where Stein identities are utilized for improved estimation performance. The construction of these Stein-type MM-estimators makes use of a weight function as implied by an appropriate form of the Stein identity. Our general approach as well as potential benefits thereof are first illustrated by the simple example of the exponential distribution. Afterward, we investigate the more sophisticated two-parameter inverse Gaussian distribution and the two-parameter negative-binomial distribution in great detail, together with illustrative real-world data examples. Given an appropriate choice of the respective weight functions, their Stein-MM estimators, which are defined by simple closed-form formulas and allow for closed-form asymptotic computations, exhibit a better performance regarding bias and mean squared error than competing estimators.
Description
This article is licensed under a Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/).
Version
Published version
Access right on openHSU
Metadata only access
Open Access Funding
Springer Nature (DEAL)