A note on the U,V method of estimation

TL;DR

This paper examines the U,V estimation method, highlighting its unbiasedness and admissibility properties for different functions and loss functions, with implications for practical applications.

Contribution

It analyzes the admissibility of V estimators in the U,V method, showing that some are inadmissible under certain loss functions while others are admissible.

Findings

V estimator is inadmissible for one U function under broad loss functions.

V estimator is admissible for another U function under squared error loss.

The paper clarifies conditions affecting the optimality of U,V estimators.

Abstract

The U,V method of estimation provides unbiased estimators or predictors of random quantities. The method was introduced by Robbins \citer3 and subsequently studied in a series of papers by Robbins and Zhang. (See Zhang \citer5.) Practical applications of the method are featured in these papers. We demonstrate that for one U function (one for which there is an important application) the V estimator is inadmissible for a wide class of loss functions. For another important U function the V estimator is admissible for the squared error loss function.