Asymptotic behavior of polynomial Pitman estimators

The asymptotic normality of polynomial Pitman estimators for the location parameter is proved, the principal term of the formula for the variance of these estimators is obtained, and certain characterization problems are considered that occur in the study of polynomial Pitman estimators.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 43, pp. 30–39, 1974.