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

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.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.

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分类依据与纠错

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

代码、数据与补充材料

P{X<Y} 的最小方差无偏估计量的容许性与极小极大性

原文摘要

同方向的基础文献

相关领域论文

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相关领域论文

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