论文标题
多输出回归和MANOVA的完全无分配中心排名测试
Fully distribution-free center-outward rank tests for multiple-output regression and MANOVA
论文作者
论文摘要
将基于等级的推断扩展到多元设置，例如具有未指定D维误差密度的多输出回归或MANOVA，在半个多世纪以来一直是一个空旷的问题。到目前为止，迄今为止提出的许多解决方案都没有享受分配繁琐和效率的结合，这使得基于等级的推理成为单变量环境中的成功工具。最近引入了基于测量运输思想的中心向外多变量等级和标志的概念。中心向外排名和标志不仅是不含分布的分布，而且在尺寸d> 1中实现了传统单变量等级的（基本）最大辅助性能，因此携带样本中所有可用的“无分配信息”。我们在这里得出了Hájek表示和渐近正态性结果，用于建造多输出回归和MANOVA的中心级别等级测试。当基于适当的球形分数时，这些完全无分布的测试在相应的模型中实现了参数效率。
Extending rank-based inference to a multivariate setting such as multiple-output regression or MANOVA with unspecified d-dimensional error density has remained an open problem for more than half a century. None of the many solutions proposed so far is enjoying the combination of distribution-freeness and efficiency that makes rank-based inference a successful tool in the univariate setting. A concept of center-outward multivariate ranks and signs based on measure transportation ideas has been introduced recently. Center-outward ranks and signs are not only distribution-free but achieve in dimension d > 1 the (essential) maximal ancillarity property of traditional univariate ranks, hence carry all the "distribution-free information" available in the sample. We derive here the Hájek representation and asymptotic normality results required in the construction of center-outward rank tests for multiple-output regression and MANOVA. When based on appropriate spherical scores, these fully distribution-free tests achieve parametric efficiency in the corresponding models.
