论文检索

摘要暂缺

与 U 过程相关的估计量及其多元中位数应用：渐近正态性AI 解读

If a criterion function $g(x_1, \ldots, x_m; \theta)$ depends on $m > 1$ samples, then a natural estimator of $\arg \max P^mg(x_1, \ldots, x_m; \theta)$ is the $\arg \max$ of a $U$-process. It is observed that, under suitable conditions, these estimators are asymptotically normal. This is then applied to prove asymptotic normality of Liu's simplical median and of Oja's medians in $\mathbb{R}^d$.

U 统计量与 V 统计量的自助法AI 解读

Bootstrap distributional limit theorems for $U$ and $V$ statistics are proved. They hold a.s., under weak moment conditions and without restrictions on the bootstrap sample size (as long as it tends to $\infty$), regardless of the degree of degeneracy of $U$ and $V$. A testing procedure based on these results is outlined.

单变量连续分布对称性的若干自助法检验AI 解读

The Kolmogorov distance between the empirical $\operatorname{cdf} F_n$ and its symmetrization $sF_n$ with respect to an adequate estimator of the center of symmetry of $P$ is a natural statistic for testing symmetry. However, its limiting distribution depends on $P$. Using critical values from the symmetrically bootstrapped statistic (where the resampling is made from $sF_n$) produces tests that can be easily implemented and have asymptotically the correct levels as well as…

均值 Bootstrap 的必要条件AI 解读

It is proved that $EX^2 < \infty$ is necessary for a very mild form of the bootstrap of the mean to work a.s. and that $X$ must be in the domain of attraction of the normal law if a.s. is weakened to "in probability."

摘要暂缺