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 differe nce 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 par ameter theta, cover a broad range of nonlinear (and linear) time serie s and stochastic process models. Herein strong consistency and asympto tic normality of the least squares estimate of theta in these stochast ic regression models are established. In the linear case f(i)(theta) = theta(T) psi(i), they reduce to known results on the linear least squ ares 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).