论文标题
基于等级间距的精确且任意准确的非参数两样本测试
Exact and arbitrarily accurate non-parametric two-sample tests based on rank spacings
论文作者
论文摘要
得出非参数检验的一种常见方法是根据样本等级重新重新制定参数测试。尽管无分布（即使在有限样品中），但所得的测试通常显示出显着的渐近功率特性，通常与其参数对应物的效率相匹配。从经验上讲，这些有利的功率属性也已证明在非反应性方案中持续存在，从而促使对基于等级的统计数据的有限样本特征的需求。在这里，我们为加权$ p $ norms的等级间距的家族提供了这种特征，其中包括Mann-Whitney，Dixon及其各种概括的经典测试。对于$ p = 1 $，我们为所涉及的分布提供了精确的表达式，而对于$ p> 1 $，我们描述了相关的力矩序列并得出算法以快速稳定的方式从这些序列中恢复了兴趣分布。我们使用此框架来开发一个新的非参数测试家族，反映了广义似然比的特性，证明了Dixon's和Greenwood的统计数据的新尾巴界限，并证明了先前提出的关于基于等级的测试的全球效率，该猜想是针对$ f $ f $ f $ the scale-fast the scale-fact the scale-fact of cable-feast of calial-for的效率。
A common method for deriving non-parametric tests is to reformulate a parametric test in terms of sample ranks. Despite being distribution free (even in finite samples), the resulting tests often display remarkable asymptotic power properties, typically matching the efficiency of their parametric counterpart. Empirically, these favorable power properties have been shown to persist in non-asymptotic regimes as well, prompting the need for finite-sample characterizations of the corresponding rank-based statistics. Here, we provide such characterization for the family of weighted $p$-norms of rank spacings, which includes the classical tests of Mann-Whitney, Dixon, and various generalizations thereof. For $p=1$, we provide exact expressions for the involved distributions, while for $p>1$ we describe the associated moment sequences and derive an algorithm to recover the distributions of interest from these sequences in a fast and stable manner. We use this framework to develop a new family of non-parametric tests mirroring properties of generalized likelihood-ratios, prove new tail bounds for Dixon's and Greenwood's statistics, and prove a previously formulated conjecture regarding the global efficiency of rank-based tests against the $F$-test in the context of scale-families.
