## The Annals of Statistics

### Admissibility and Minimaxity of the UMVU Estimator of $P\{X < Y\}$

#### Abstract

Suppose that $X_1,\ldots, X_m$ are i.i.d. from a continuous distribution function $F$ and $Y_1,\ldots, Y_n$ are i.i.d. from a continuous distribution function $G; X$'s and $Y$'s are independent. A minimum variance unbiased estimator of $P\{X < Y\}$ is the Mann-Whitney statistic. We show that the Mann-Whitney statistic is admissible under a class of weighted squared error losses and is minimax under a proper weighted squared error loss.

#### Article information

Source
Ann. Statist., Volume 23, Number 2 (1995), 598-607.

Dates
First available in Project Euclid: 11 April 2007

https://projecteuclid.org/euclid.aos/1176324538

Digital Object Identifier
doi:10.1214/aos/1176324538

Mathematical Reviews number (MathSciNet)
MR1332584

Zentralblatt MATH identifier
0824.62008

JSTOR
Yu, Qiqing; Govindarajulu, Z. Admissibility and Minimaxity of the UMVU Estimator of $P\{X &lt; Y\}$. Ann. Statist. 23 (1995), no. 2, 598--607. doi:10.1214/aos/1176324538. https://projecteuclid.org/euclid.aos/1176324538