## The Annals of Statistics

### A Large Deviation Result for Parameter Estimators and its Application to Nonlinear Regression Analysis

#### 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).

#### Article information

Source
Ann. Statist., Volume 15, Number 3 (1987), 1031-1049.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176350491

Digital Object Identifier
doi:10.1214/aos/1176350491

Mathematical Reviews number (MathSciNet)
MR902244

Zentralblatt MATH identifier
0661.62021

JSTOR