Exact computation of bivariate projection depth and the Stahel-Donoho estimator

Authors:
Yijun Zuo;Shaoyong Lai
Affiliations:
School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, Sichuan 610074, China and Department of Statistics and Probability, Michigan State University, East Lansi ...;School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, Sichuan 610074, China
Venue:
Computational Statistics & Data Analysis
Year:
2011

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Abstract

The idea of data depth provides a new and promising methodology for multivariate nonparametric analysis. Nevertheless, the computation of data depth and the depth function has remained as a very challenging problem which has hindered the methodology from becoming more prevailing in practice. The same is true for the powerful Stahel-Donoho (S-D) estimator. Here, we present an exact algorithm for the computation of the bivariate projection depth (PD) of data points and consequently of the S-D estimator.