ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

12. Probability and Statistics

1991 MS Classification: Knopov, P. S., V. M. Glushkov Institute of Cybernetics of the Academy of Sciences of Ukraine Asymptotic Properties of Non-Linear Estimators for Some Non-Stationary Regression Models We consider the problem of minimization of functional F_{T} (x) = \frac{1}{T} ∫_{0}^{T} f(t, x, ξ_{t})dt, where \{ξ_{t} ∈ R^{m}, m ≥ 1\} is some stationary process satisfying strong mixing condition, x ∈ J, where J is some closed subset of R^{p}, p ≥ 1, function f(x, y, z) : R^{+} × J × R^{m} → R^{+}, R^{+} = [0, ∞). Let x_{T} = arg min F_{T} (x). Values x_{T} asymptotic distribution is find and x_{T} strong consistity is proved.