Density Prediction and the Stein Phenomenon

Malay Ghosh (), Tatsuya Kubokawa () and Gauri Sankar Datta ()
Additional contact information
Malay Ghosh: University of Florida
Tatsuya Kubokawa: University of Tokyo
Gauri Sankar Datta: University of Georgia

Sankhya A: The Indian Journal of Statistics, 2020, vol. 82, issue 2, No 3, 330-352

Abstract: Abstract The Stein phenomenon is a path-breaking discovery in mathematical statistics in the last century. A large number of researchers followed Stein’s footsteps and developed a wide variety of minimax shrinkage point estimators of a multivariate normal mean vector, each dominating the sample mean. More recently, the problem resurfaced, but this time with minimax shrinkage predictive density estimation, illustrating once again the Stein phenomenon In this review paper, we discuss parallel developments for normal and Poisson distributions under the Kullback-Leibler and more general divergence losses.

Keywords: Divergence loss; Dominance property; Empirical Bayes; Hellinger-Bhattacharyya divergence; Kullback-Leibler divergence; Minimaxity; Normal distribution; Poisson distribution; Risk function; Shrinkage estimator; Simultaneous estimation; Superharmonic; Primary 62C20; Secondary 62F10 (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/s13171-019-00186-z 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:sankha:v:82:y:2020:i:2:d:10.1007_s13171-019-00186-z

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/13171

DOI: 10.1007/s13171-019-00186-z

Access Statistics for this article

Sankhya A: The Indian Journal of Statistics is currently edited by Dipak Dey

More articles in Sankhya A: The Indian Journal of Statistics from Springer, Indian Statistical Institute
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().