Consistency Of The Least Squares Estimator In Nonlinear Regression Model

In nonlinear regression model, θn is the least squares estimator for parameter θ, its consistency problem has a important background of statistic application, so its consistency problem has been studied by many statistic scientists, and has been resolved more perfectly.When model errors {εn} has independently identical distribution , and its /th absolute moments are finite, for t≥2, Ivanov (1976) has obtained the probability inequality about deviation of θn and θ ; However , When model errors {εn} are φ>-mixing or strong mixingsequences, Prakasa Rao (1984) improved the result of Ivanov, but the assumptions on moments and mixing coefficients of {εn} are strict.Assuming that the t th absolute moments of the model errors {εn} are finite , for t≥>2 and the errors satisfy general dependent conditions, we obtain the same probability inequality as that in Ivanov (1976) which has independent identically distributed errors, then we also obtain strong consistency and strong consistency rate of θn For 1