Admissibility and Minimaxity of the UMVU Estimator of $P\{X < Y\}$
Yu, Qiqing ; Govindarajulu, Z.
Ann. Statist., Tome 23 (1995) no. 6, p. 598-607 / Harvested from Project Euclid
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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.
Publié le : 1995-04-14
Classification:  Admissibility,  minimaxity,  multinomial distribution,  conditional Bayes estimator,  62C15,  62C10 
@article{1176324538,
     author = {Yu, Qiqing and Govindarajulu, Z.},
     title = {Admissibility and Minimaxity of the UMVU Estimator of $P\{X < Y\}$},
     journal = {Ann. Statist.},
     volume = {23},
     number = {6},
     year = {1995},
     pages = { 598-607},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176324538}
}

Yu, Qiqing; Govindarajulu, Z. Admissibility and Minimaxity of the UMVU Estimator of $P\{X < Y\}$. Ann. Statist., Tome 23 (1995) no. 6, pp.  598-607. http://gdmltest.u-ga.fr/item/1176324538/