Large deviation for a least squares estimator in a nonlinear regression model

By using a large deviation theory of the stochastic process and the moment information of errors, some large deviation results for the least squares estimator θn in a nonlinear regression model are obtained when errors satisfy some general conditions. For some p>1, examples are presented to show that our results can be used in the case for supn≥1E|ξn|p=∞ and a better bound can be obtained in the case for supn≥1E|ξn|p<∞. Our results generalize and improve the corresponding ones.