Weak convergence of randomly stopped log-likelihood ratio statistic to mixed Gaussian process. (English) Zbl 0777.60021

Basu, A. K.; Bhattacharya, Debasis

Bull., Calcutta Stat. Assoc. 39, No. 155-156, 137-149 (1990).

Parametric families of general discrete time stochastic processes are considered. The main result of the paper states that, under appropriate regularity assumptions, certain random fields associated with the randomly stopped log-likelihood ratio process converge weakly to a mixed Gaussian shift process (Theorem 2.4). That result is applied for establishing the convergence of moments of sequential ML estimators. Explosive autoregressive processes of first order and supercritical Galton-Watson branching processes are also treated as examples.

Reviewer: T.F.Móri (Budapest)

MSC:

60F05	Central limit and other weak theorems
62F12	Asymptotic properties of parametric estimators

Keywords:

random fields; log-likelihood ratio process; Gaussian shift process; autoregressive processes; supercritical Galton-Watson branching processes