论文检索

摘要暂缺

秩检验的定性稳健性AI 解读

An asymptotic notion of robust tests is studied which is based on the requirement of equicontinuous error probabilities. If the test statistics are consistent, their robustness in Hampel's sense and robustness of the associated tests turn out to be equivalent. Uniform extensions are considered. Moreover, test breakdown points are defined. The main applications are on rank statistics: they are generally robust, under a slight condition even uniformly so; their points of final…

稳健估计中的局部渐近极小极大性与可容许性AI 解读

For a particular pseudoloss function, local asymptotic minimaxity and admissibility in the sense of Hajek and Le Cam are studied when probability measures are replaced by certain capacities ($\epsilon$-contamination, total variation). A minimax bound for arbitrary estimator sequences is established, admissibility of minimax estimators is proved, and it is shown that minimax estimators must necessarily have an asymptotic expansion in terms of a truncated logarithmic…

单样本与双样本秩检验对粗大误差的稳健性AI 解读

The classical nonparametric hypotheses of symmetry and equality of distribution functions are extended to hypotheses of approximate symmetry and approximate equality, by allowing for gross errors, which is indispensable for practical applications. It is shown that for these hypotheses one- and two-sample rank statistics maintain their distribution freeness, which now refers to their stochastically extreme laws. These laws are evaluated asymptotically, also under similarly…

从稳健检验导出的估计量AI 解读

In this paper, an asymptotic minimax theory for robust estimation of a one-dimensional parameter is derived, which is an asymptotic counterpart, and generalization to an arbitrary parameter, of Huber's finite sample minimax theory for the location case. A particular variability measure and results from robust asymptotic testing are employed. The results show a relationship of this approach to Hampel's local theory of robustness.

一个稳健的渐近检验模型AI 解读

In order to obtain quantitative results about the influence of outliers on tests, their maximum size and minimum power over certain neighborhoods are evaluated asymptotically. The neighborhoods are defined in terms of $\varepsilon$-contamination and total variation, the tests considered are based on statistics $n^{-\frac{1}{2}} \sum^n_{i=1} IC(x_i), IC$ a rather arbitrary function. Furthermore, the unique $IC^\ast$ is determined that leads to a maximin test with respect to…

特殊容量下的最不利分布对AI 解读

The least favorable pair (LFP) that Huber (1965), (1968) wrote down when he considered minimax test problems between neighborhoods of single probability measures $P_0, P_1$ defined in terms of $\varepsilon$-contamination and total variation is a canonical but only one possible choice of an LFP. We treat these neighborhoods by means of special capacities. The minimax test statistic is obtained by explicitly solving a minimization program, all LFP's are characterized by their $(P_0 + P_1)$…