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简单回归模型中的 Brown–Mood 型中位数估计量AI 解读

In the context of simple linear regression we investigate a class of estimators for the parameters which contains the Brown-Mood estimators. We derive the asymptotic efficiency properties of the class of slope estimators and find the most efficient slope estimator. This estimator is shown to have efficiency properties analogous to those of other median estimators for slope found in the literature. The equations which define the optimal estimators are median analogues of the…

缩减 U 统计量与 Hodges–Lehmann 估计量AI 解读

A reduced $U$-statistic (of order 2) is defined as the sum of terms $f(X_i, X_j),$ where $f$ is a symmetric function, $(X_1, \cdots, X_N)$ are independent and identically distributed (i.i.d.) random variables (rv's), and $(i,j)$ are drawn from a restricted, though balanced, set of pairs. (A $U$-statistic corresponds to summation over all $(i, j)$ pairs.) A limit normal distribution is found for the reduced $U$-statistic, and it follows that estimates based on reduced $U$-stat…