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Kaplan–Meier 估计量一类泛函的几乎必然渐近表示AI 解读

This paper deals with censored data estimation of a general class of von Mises-type functionals of the survival time distribution $F$. Conditions are given under which an almost sure asymptotic representation holds for the estimator, obtained by applying the same functional to $\hat{F}_n$, the product-limit estimator of Kaplan and Meier.

一类统计泛函的渐近正态性及其离散程度度量应用AI 解读

A general class of statistical functionals is introduced and the asymptotic normality of the corresponding estimators is established. Included are certain measures of spread, proposed by Bickel and Lehmann (1979), for which the asymptotic distribution theory has been an open problem. The proofs involve some new results, of independent interest, for empirical and quantile processes.

学生化 U 统计量的正态近似阶AI 解读

Let $U_N$ be a one sample $U$-statistic with kernel $h$ of degree two, such that $Eh(X_1, X_2) = \vartheta$ and $\operatorname{Var} E\lbrack h(X_1, X_2)\mid X_1 \rbrack > 0$. It is shown that for a studentized $U$-statistic $\sup_x|P(N^{1/2}S^{-1}_N(U_N - \vartheta) \leqslant x) - \Phi(x)| = O(N^{-1/2})$ as $N \rightarrow \infty$, where $N^{-1}S^2_N = 4N^{-1}(N - 1)(N - 2)^{-2}\sum^N_{i=1} \lbrack (N - 1)^{-1} \sum_{j\neq i} h(X_i, X_j) - U_N \rbrack^2$ is the jackknife…