On the probability of large deviations of an estimator of a nonlinear regression parameter in Hilbert space. (English. Russian original) Zbl 0699.62066

Kukush, A. G.

Theory Probab. Math. Stat. 40, 51-58 (1990); translation from Teor. Veroyatn. Mat. Stat., Kiev 40, 44-51 (1989).

Summary: Estimation of the parameter constructed in accordance with the weighted least squares method in a nonlinear regression model in a Hilbert space is studied. Exponential bounds are obtained on the probability of large deviations with entropy constraints from above on the regression function. From these bounds under minimal constraints from below one can deduce the consistency of the estimators of some of the parameters. For a weakly dependent noise, polynomial bounds on the probability of large deviations are presented.

MSC:

62J02	General nonlinear regression
60F10	Large deviations
62H12	Estimation in multivariate analysis

Keywords:

Gaussian noise; weighted least squares method; Hilbert space; Exponential bounds; entropy constraints; consistency; weakly dependent noise; polynomial bounds