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一致随机序约束下某类分布一致估计量的渐近分布理论AI 解读

We identify the asymptotic behavior of the estimators proposed by Rojo and Samaniego and Mukerjee of a distribution $F$ assumed to be uniformly stochastically smaller than a known baseline distribution $G$.We show that these estimators are $\sqrt{n}$-convergent to a limit distribution with mean squared error smaller than or equal to the mean squared error of the empirical survival function. By examining the mean squared error of the limit distribution, we are able to…

基于凸核的 M 估计量渐近理论AI 解读

We study the convergence in distribution of M -estimators over a convex kernel. Under convexity, the limit distribution of M -estimators can be obtained under minimal assumptions. We consider the case when the limit is arbitrary, not necessarily normal. If some Taylor expansions hold, the limit distribution is stable. As an application, we examine the limit distribution of M -estimators for the multivariate linear regression model. We obtain the distributional convergence of…

Lp 回归估计量的 Bahadur–Kiefer 表示AI 解读

We consider the following linear regression model: where are independent and identically distributed random variables, Y i , is real, Z i has values in R m , U i , is independent of Z i , and θ 0 is an m -dimensional parameter to be estimated. The L p estimator of θ 0 is the value 6n such that Here, we will give the exact Bahadur-Kiefer representation of θn, for each p ≥ 1. Explicitly, we will see that, under regularity conditions, where and c is a positive constant, which…

U 分位数自助法的渐近精度AI 解读

The order of the Kolmogorov-Smirnov distance for the bootstrap of $U$-quantiles is considered. We observe that the order of the bootstrap of $U$-quantiles depends on the order of the local variance of the first term of the Hoeffding decomposition at the $U$-quantile. This order can be smaller than the order of the bootstrap of quantiles: $U$-quantiles can be smoother than quantiles.

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…