Online stochastic Newton methods for estimating the geometric median and applications

IF 1.4 3区 数学 Q2 STATISTICS & PROBABILITY
Antoine Godichon-Baggioni , Wei Lu
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引用次数: 0

Abstract

In the context of large samples, a small number of individuals might spoil basic statistical indicators like the mean. It is difficult to detect automatically these atypical individuals, and an alternative strategy is using robust approaches. This paper focuses on estimating the geometric median of a random variable, which is a robust indicator of central tendency. In order to deal with large samples of data arriving sequentially, online stochastic Newton algorithms for estimating the geometric median are introduced and we give their rates of convergence. Since estimates of the median and those of the Hessian matrix can be recursively updated, we also determine confidences intervals of the median in any designated direction and perform online statistical tests.

估计几何中值的在线随机牛顿方法及其应用
在大量样本中,少数个体可能会破坏基本的统计指标,如平均值。要自动检测出这些非典型个体是很困难的,另一种策略是使用稳健方法。本文的重点是估计随机变量的几何中值,它是中心倾向的稳健指标。为了处理连续到达的大量数据样本,本文介绍了估算几何中值的在线随机牛顿算法,并给出了其收敛率。由于中位数和黑森矩阵的估计值可以递归更新,我们还确定了中位数在任意指定方向上的置信区间,并进行了在线统计检验。
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来源期刊
Journal of Multivariate Analysis
Journal of Multivariate Analysis 数学-统计学与概率论
CiteScore
2.40
自引率
25.00%
发文量
108
审稿时长
74 days
期刊介绍: Founded in 1971, the Journal of Multivariate Analysis (JMVA) is the central venue for the publication of new, relevant methodology and particularly innovative applications pertaining to the analysis and interpretation of multidimensional data. The journal welcomes contributions to all aspects of multivariate data analysis and modeling, including cluster analysis, discriminant analysis, factor analysis, and multidimensional continuous or discrete distribution theory. Topics of current interest include, but are not limited to, inferential aspects of Copula modeling Functional data analysis Graphical modeling High-dimensional data analysis Image analysis Multivariate extreme-value theory Sparse modeling Spatial statistics.
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