Orlovsky I. Asymptotic properties of M-estimates of nonlinear regression model parameters

The sufficient conditions of strong consistency of M-estimates of nonlinear regression model parameters with continuous time and weak dependent stationary noise or long-range dependent Gaussian stationary noise are obtained. Two cases have been considered: the observations are carrying out according to some regression experiment design and the case when there is no such a design. It is found the sufficient conditions of asymptotic normality of M-estimates for models with continuous time and weak dependent stationary Gaussian noise. The sufficient conditions of asymptotic normality of Lp-estimates of nonlinear regression model parameters with continuous time and long-range dependent stationary Gaussian noise are obtained. Besides, it is found the sufficient conditions of consistency and asymptotic normality of Koenker-Bassett estimates of nonlinear regression model parameters with discrete time and independent identically distributed nonsymmetrical observation errors.