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加权中位数回归估计AI 解读

In the simple linear regression problem $\{Y_i = \alpha + \beta x_i + e_i i = 1,\cdots, n, e_i$ i.i.d. $\sim F$ continuous, $x_1 \leqq \cdots \leqq x_n$ known, $\alpha, \beta$ unknown$\}$ we investigate the following type of estimator: To each $s_{ij} = (Y_j - Y_i)/(x_j - x_i)$ with $x_i < x_j$ attach weight $w_{ij}$ and as estimator for $\beta$ consider the median of this weight distribution over the $s_{ij}$. A confidence interval for $\beta$ is found by taking certain…

有效位置估计量的比较AI 解读

For a given sufficiently regular distribution $F$ two efficient location estimators are given. One is a linear combination of order statistics, called $L(F)$, and the other is an estimator derived from a rank test, called $R(F)$. The asymptotic variance of both estimators is then compared for various underlying distributions $H$ and it is shown that the asymptotic variance of $R(F)$ is never larger than the one of $L(F)$.