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September, 1987 A Large Deviation Result for Parameter Estimators and its Application to Nonlinear Regression Analysis
Arthur Sieders, Kacha Dzhaparidze
Ann. Statist. 15(3): 1031-1049 (September, 1987). DOI: 10.1214/aos/1176350491

Abstract

Elaborating on the work of Ibragimov and Has'minskii (1981) we prove a law of large deviations (LLD) for $M$-estimators, i.e., those estimators which maximize a functional, continuous in the parameter, of the observations. This LLD is applied, using the results of Petrov (1975), to the problem of parametrical nonlinear regression in the situation of discrete time, independent errors and regression functions which are continuous in the parameter. This improves a result of Prakasa Rao (1984).

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Arthur Sieders. Kacha Dzhaparidze. "A Large Deviation Result for Parameter Estimators and its Application to Nonlinear Regression Analysis." Ann. Statist. 15 (3) 1031 - 1049, September, 1987. https://doi.org/10.1214/aos/1176350491

Information

Published: September, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0661.62021
MathSciNet: MR902244
Digital Object Identifier: 10.1214/aos/1176350491

Subjects:
Primary: 60F10
Secondary: 62F12, 62J02

Rights: Copyright © 1987 Institute of Mathematical Statistics

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Vol.15 • No. 3 • September, 1987
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