Abstract
In a “errors-in-variables” model a local asymptotic minimax risk bound is established. In the case of bounded loss functions it is attained by the maximum likelihood estimator. Furthermore, a certain modified estimator is constructed, which is optimal in the minimax sense for any loss function with polynomial major, possible unbounded.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Ibragiraov I. A. Khasminski R. Z. (1983): On the efficient estimation in the presence of an infinite dimensional nuisance parameter (in Russian). In: Prooceedings of the USSR — Japan Symposium on Frobality theory and Mathematical Statistics, Tiblissi, Springer Lecture notes in statistics, to appear
Kumon M. Amari S. (1984): Estimation of a structural parameter the presence of a large number of nuisance parameters. Biometrika 71, 445–459
Nussbaum. (1979): Asymptotic efficiency of estimators of a multivariate linear functional relation. Math. Operationsforsch. Statist. Ser. Statist. 10, 505–527
Nussbaum. (1984): An asymptotic minimax risk bound for the estimation of a linear functional relation-ship. J. Multivariae Anal. 13, 300–314.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1988 Academia, Publishing House of the Czechoslovak Academy of Sciences, Prague
About this chapter
Cite this chapter
Nussbaum, M., Zwanzig, S. (1988). A Minimax Result in a Model with Infinitely Many Nuisance Parameters. In: Transactions of the Tenth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes. Transactions of the Tenth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes, vol 10A-B. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9913-4_27
Download citation
DOI: https://doi.org/10.1007/978-94-010-9913-4_27
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-9915-8
Online ISBN: 978-94-010-9913-4
eBook Packages: Springer Book Archive