Explicit estimators of an unknown parameter in a power 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 meets 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 estimators are proved to be asymptotically normal under wide assumptions. The asymptotic normality of these estimators is proved and the assessment with the minimum asymptotic variance is found. Earlier such explicit estimators were known only for two equations of non-linear regression.