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一步与两步 M 估计量的收敛速度：最大似然与 Pitman 估计的应用AI 解读

A one-step version $M^{(1)}_n$ and a two-step version $M^{(2)}_n$ of a general $M$-estimator $M_n$ are suggested such that $M_n - M^{(1)}_n = O_p(n^{-1})$ and $M_n - M^{(2)}_n = O_p(n^{-3/2})$ for every $n^{1/2}$-consistent initial estimator and under some regularity conditions. In the special case of maximum likelihood estimation, this among other yields that the second-order efficiency properties of $M^{(2)}_n$ coincide with those of $M_n$. An application to the Pitman…

U 统计量的 Edgeworth 展开AI 解读

It is shown that, under some regularity conditions on the kernel, a one-sample $U$-statistic with kernel of degree two admits an asymptotic expansion with remainder term $o(N^{-1})$.