Asymptotic expansions connected with an estimator of the variance of the observation error for a model of “signal plus noise”. (English. Russian original) Zbl 0632.62089

Bardadym, T. A.; Ivanov, A. V.

Theory Probab. Math. Stat. 33, 11-20 (1986); translation from Teor. Veroyatn. Mat. Stat. 33, 11-20 (1985).

An asymptotic expansion is obtained for an estimator of the variance of the observation error for a nonlinear model of “signal plus noise”. The first terms of the asymptotic expansion of the bias and the variance of the error are determined.

MSC:

62M09	Non-Markovian processes: estimation
62M20	Inference from stochastic processes and prediction
62F12	Asymptotic properties of parametric estimators

Keywords:

asymptotic expansion; observation error; nonlinear model; signal plus noise; bias; variance