Adaptive Multiple Decision Procedures for Exponential Families

Rukhin, Andrew L.

doi:10.1007/978-1-4612-2308-5_7

Adaptive Multiple Decision Procedures for Exponential Families

Andrew L. Rukhin⁴

Chapter

532 Accesses

Part of the book series: Statistics for Industry and Technology ((SIT))

Abstract

The asymptotic behavior of multiple decision procedures is studied when the underlying distributions belong to an exponential family. An adaptive procedure must be asymptotically optimal for each value of the unknown nuisance parameter, on which it does not depend. A necessary and sufficient condition for the existence of such a procedure is discussed. The regions of the parameter space, where the traditional overall maximum likelihood rule is adaptive, are described. The examples of a normal family and a family of gamma-distributions are considered in detail.

This is a preview of subscription content, log in via an institution.

Chapter: USD 29.95; Price excludes VAT (USA)

eBook: USD 39.99; Price excludes VAT (USA)

Softcover Book: USD 54.99; Price excludes VAT (USA)

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

References

Bickel, P. A., Klaassen, C. A. J., Ritov, J. and Wellner, J. A. (1993). Efficient and Adaptive Estimation for Semiparametric Models, Baltimore: Johns Hopkins University Press.
MATH Google Scholar
Chernoff, H. (1956). Large-sample theory: Parametric case, Annals of Mathematical Statistics, 27, 1–22.
Article MathSciNet MATH Google Scholar
Krafft, O. and Puri, M. L. (1974). The asymptotic behavior of the minimax risk for multiple decision problems, Sankhya A, 36, 1–12.
MathSciNet MATH Google Scholar
Renyi, A. (1970). On some problems of statistics from the point of view of information theory, In Proceedings of the Colloquium on Information Theory-2, pp. 343–357, Budapest, Hungary: Bolyai Mathematical Society.
Google Scholar
Rukhin, A. L. (1982). Adaptive procedures for a finite number of probability distributions families, In Proceedings of Third Purdue Symposium on Decision Theory-1 (Eds. S. S. Gupta and J. O. Berger), pp. 269–286, New York: Academic Press.
Google Scholar
Rukhin, A. L. (1984). Adaptive classification procedures, Journal of the American Statistical Association, 79, 415–422.
Article MathSciNet MATH Google Scholar
Stein, C. (1957). Efficient nonparametric testing and estimation, In Proceedings of Third Berkeley Symposium on Mathematical Statistics and Probability-1, pp. 187–196, Berkeley: University of California Press.
Google Scholar

Download references

Author information

Authors and Affiliations

University of Maryland Baltimore County, Baltimore, MD, USA
Andrew L. Rukhin

Authors

Andrew L. Rukhin
View author publications
You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

Department of Math, Southern Illinois University, 62901-4408, Carbondale, IL, USA
S. Panchapakesan
Department of Mathematics and Statistics, McMaster University, L8S 4K1, Hamilton, Ontario, Canada
N. Balakrishnan

Rights and permissions

Reprints and permissions

Copyright information

About this chapter

Cite this chapter

Rukhin, A.L. (1997). Adaptive Multiple Decision Procedures for Exponential Families. In: Panchapakesan, S., Balakrishnan, N. (eds) Advances in Statistical Decision Theory and Applications. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2308-5_7

Download citation

DOI: https://doi.org/10.1007/978-1-4612-2308-5_7
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-7495-7
Online ISBN: 978-1-4612-2308-5
eBook Packages: Springer Book Archive

Publish with us

Policies and ethics