对称独立分量模型中基于符号秩的半参数有效推断
Semiparametrically efficient inference based on signed ranks in symmetric independent component models
摘要：
我们考虑半参数位置-散布模型，其$p$ -变量观测被获得为$X=ΛZ+μ$，其中$μ$是$p$ -向量，$Λ$是满秩$p\times p$矩阵，并且（未观测的）随机$p$ -向量$Z$具有居中且相互独立但未指定的边缘。与盲源分离和独立分量分析（ICA）一样，本文中感兴趣的参数是$Λ$。在$n$ i.i.d.的$X$的副本，我们开发，在$Z$的对称性假设下，符号秩单样本检验和估计程序$Λ$。我们利用该模型的均匀局部性和渐近正态性（ULAN）来定义在正确指定的密度下半参数有效的符号秩程序。然而，通常在基于秩的推理，所提出的程序仍然有效（正确的渐近大小下的零，假设检验，和根$n$一致性，点估计）在一个非常广泛的密度范围。我们推导出所提出的方法的渐近性质，并通过模拟研究其有限样本行为。
英文摘要：
We consider semiparametric location-scatter models for which the $p$-variate observation is obtained as $X=ΛZ+μ$, where $μ$ is a $p$-vector, $Λ$ is a full-rank $p\times p$ matrix and the (unobserved) random $p$-vector $Z$ has marginals that are centered and mutually independent but are otherwise unspecified. As in blind source separation and independent component analysis (ICA), the parameter of interest throughout the paper is $Λ$. On the basis of $n$ i.i.d. copies of $X$, we develop, under a symmetry assumption on $Z$, signed-rank one-sample testing and estimation procedures for $Λ$. We exploit the uniform local and asymptotic normality (ULAN) of the model to define signed-rank procedures that are semiparametrically efficient under correctly specified densities. Yet, as is usual in rank-based inference, the proposed procedures remain valid (correct asymptotic size under the null, for hypothesis testing, and root-$n$ consistency, for point estimation) under a very broad range of densities. We derive the asymptotic properties of the proposed procedures and investigate their finite-sample behavior through simulations.
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