论文检索

直接利用回归分位数构造线性模型置信集AI 解读

Direct use of the empirical quantile function provides a standard distribution-free approach to constructing confidence intervals and confidence bands for population quantiles. We apply this method to construct confidence intervals and confidence bands for regression quantiles and to construct prediction intervals based on sample regression quantiles. Comparison of the direct method with the studentization and the bootstrap methods are discussed. Simulation results show that…

统计检验的崩溃稳健性AI 解读

Power and level breakdown functions of a test statistic are introduced to obtain a unified analysis of local stability (as typified by the influence function) and global stability (as illustrated by the breakdown point). The power breakdown function gives the amount of contamination of each alternative distribution that can carry the test statistic to a null value. The level breakdown function gives the amount of contamination of a null distribution that can carry the test…

利用广义矩空间方法最大化M估计量的方差AI 解读

The problem considered is that of optimizing a function of a finite number of linear functionals over an infinite dimensional convex set $S$. It is shown that under some reasonably general conditions the method of moment spaces can be used to reduce the problem to one of optimizing over a simple finite dimensional set (generally a set of convex combinations of extreme points of $S$). The results are applied to finding the maximum asymptotic variance of M-estimators over…

关于相依情形下稳健估计的进一步讨论AI 解读

Results of an earlier paper giving first order optimal robust $M$-estimators of a location parameter in certain dependent situations are extended to the case where the dependency can be modeled by a symmetric form of a $(2k + 1)$st order moving average scheme. It is also shown that the results can not be extended to finding second order optimal $M$-estimators. That is, no $M$-estimators can be optimal to the second order unless they explicitly adapt themselves to the assumed…

相关样本情形下的稳健估计AI 解读

To analyze the effect of correlation in random samples on the performance of estimators of location, small correlation approximations for the asymptotic variance are found. Approximately optimal estimators (in the asymptotic minimax sense of Huber) are presented and compared to other estimators in terms of maximum asymptotic variance over the class of $\varepsilon$-contaminated normals. The presence of relatively small correlation can drastically inflate variances, and the…

位置向量单个坐标最优不变估计量的可容许性AI 解读

In 1960, Charles Stein conjectured that the best invariant estimate of a single co-ordinate of a $p$-dimensional location parameter would be admissible if $p \leqq 3$ but inadmissible if $p \geqq 4$. This appear present a class of examples which supports Stein's conjecture.