Explicit asymptotically normal estimators of an unknown parameter in a partially linear regression problem

The problem of estimation of an unknown parameter in a special nonlinear regression problem is considered. The problem is given in the E. Z. Demidenko’s monograph as a standard example of a nonlinear regression where finding of the classical least squares estimator containes considerable computing difficulties. In the paper explicit estimators of the unknown parameter are constructed which may be represented as a ratio of two linear statistics depending on specially picked up constants. The asymptotic normality of these estimators is proved and the assessment with the minimum asymptotic variance is found. Earlier only one example of nonlinear regression problem, belonging to A. I. Sakhanenko and Yu. Yu. Linke, was known for which it was succeeded to find explicit estimators with similar properties.