摘要翻译：
基于Hallin和Paindaveine[ANN.Statist.34(2006)]中的多元符号秩和最优秩检验的概念，提出了一类用于椭圆分布形状矩阵估计的R-估计。这些R-估计在任意径向密度g下是根-n相合的，不需要任何矩假设，并且在预先给定的密度f下是半参数有效的。当基于正规分数时，它们一致地比基于经验协方差矩阵的传统正规理论估计更有效（此外，它的渐近正态性需要有限的四阶矩），而与实际的潜在椭圆密度无关。他们依赖于一个原始的基于秩的版本的Le Cam的一步方法，避免了令人不快的非参数估计交叉信息量，通常需要在R-估计的背景下。虽然它们不是严格仿射等变的，但在弱渐近意义下它们是等变的。仿真结果证实了它们的可行性和优良的有限样本性能。
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英文标题：
《Semiparametrically efficient rank-based inference for shape II. Optimal
  R-estimation of shape》
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作者：
Marc Hallin, Hannu Oja, Davy Paindaveine
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最新提交年份：
2007
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分类信息：

一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  A class of R-estimators based on the concepts of multivariate signed ranks and the optimal rank-based tests developed in Hallin and Paindaveine [Ann. Statist. 34 (2006)] is proposed for the estimation of the shape matrix of an elliptical distribution. These R-estimators are root-n consistent under any radial density g, without any moment assumptions, and semiparametrically efficient at some prespecified density f. When based on normal scores, they are uniformly more efficient than the traditional normal-theory estimator based on empirical covariance matrices (the asymptotic normality of which, moreover, requires finite moments of order four), irrespective of the actual underlying elliptical density. They rely on an original rank-based version of Le Cam's one-step methodology which avoids the unpleasant nonparametric estimation of cross-information quantities that is generally required in the context of R-estimation. Although they are not strictly affine-equivariant, they are shown to be equivariant in a weak asymptotic sense. Simulations confirm their feasibility and excellent finite-sample performances.
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PDF链接：
https://arxiv.org/pdf/708.0079