Estimating a function of scale parameter of an exponential population with unknown location under general loss function

Lakshmi Kanta Patra (), Suchandan Kayal () and Somesh Kumar ()
Additional contact information
Lakshmi Kanta Patra: Indian Institute of Petroleum and Energy
Suchandan Kayal: National Institute of Technology Rourkela
Somesh Kumar: Indian Institute of Technology Kharagpur

Statistical Papers, 2020, vol. 61, issue 6, No 11, 2527 pages

Abstract: Abstract In the present study, we consider the problem of estimating a function of scale parameter $$\ln \sigma $$ ln σ under an arbitrary location invariant bowl-shaped loss function, when location parameter $$\mu $$ μ is unknown. Various improved estimators are proposed. Inadmissibility of the best affine equivariant estimator (BAEE) of $$\ln \sigma $$ ln σ is established by deriving a Stein-type estimator. This improved estimator is not smooth. We derive a smooth estimator improving upon the BAEE. Further, the integral expression of risk difference (IERD) approach of Kubokawa is used to derive a class of improved estimators. To illustrate these results, we consider two specific loss functions: squared error and linex loss functions, and derive various estimators improving upon the BAEE. Finally, a simulation study has been carried out to numerically compare the risk performance of the improved estimators.

Keywords: Best affine equivariant estimator; Location invariant loss function; Stein’s and Brewster–Zidek’s techniques; IERD approach; Inadmissible estimators (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s00362-018-1052-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:stpapr:v:61:y:2020:i:6:d:10.1007_s00362-018-1052-7

Ordering information: This journal article can be ordered from
http://www.springer. ... business/journal/362

DOI: 10.1007/s00362-018-1052-7

Access Statistics for this article

Statistical Papers is currently edited by C. Müller, W. Krämer and W.G. Müller

More articles in Statistical Papers from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().