A robust sample spatial outlyingness function

作者：Mazumder Satyaki; Serfling Robert^*

来源：Journal of Statistical Planning and Inference, 2013, 143(1): 144-159.

DOI：10.1016/j.jspi.2012.06.017

• Multivariate analysis
• Nonparametric methods
• Robustness
• Spatial outlyingness
• Spatial quantile function
• Trimming

Sample quantile, rank, and outlyingness functions play long-established roles in univariate exploratory data analysis. In recent years, various multivariate generalizations have been formulated, among which the %26quot;spatial%26quot; approach has become especially well developed, including fully affine equivariant/invariant versions with but modest computational burden (Mottonen and Oja, 1995; Chaudhuri, 1996; Vardi and Zhang, 2000; Serfling, 2010; Oja, 2010). The only shortcoming of the spatial approach is that its robustness decreases to zero as the quantile or outlyingness level is chosen farther out from the center (Dang and Serfling, 2010). This is especially detrimental to exploratory data analysis procedures such as detection of outliers and delineation of the %26quot;middle%26quot; 50%, 75%, or 90% of the data set, for example. Here we develop suitably robust versions using a trimming approach. The improvements in robustness are illustrated and characterized using simulated and actual data. Also, as a byproduct of the investigation, a new robust, affine equivariant, and computationally easy scatter estimator is introduced.

• 出版日期2013-1