ASYMPTOTIC PROPERTIES OF NONLINEAR LEAST-SQUARES ESTIMATES IN STOCHASTIC REGRESSION-MODELS

Stochastic regression models of the form y(i) = f(i)(theta) + epsilon(i), where the random disturbances epsilon(i) form a martingale difference sequence with respect to an increasing sequence of sigma-fields {g(i)} and f(i) is a random g(i-1)-measurable function of an unknown parameter theta, cover a broad range of nonlinear (and linear) time series and stochastic process models. Herein strong consistency and asymptotic normality of the least squares estimate of theta in these stochastic regression models are established. In the linear case f(i)(theta) = theta(T) psi(i), they reduce to known results on the linear least squares estimate (Sigma(1)(n) psi(i) psi(i)(T))(-1)Sigma(1)(n) psi(i)y(i) with stochastic g(i-1)-measurable regressors psi(i).