CompPD: A MATLAB Package for Computing Projection Depth

Abstract

Since the seminal work of Tukey (1975), depth functions have proved extremely useful in robust data analysis and inference for multivariate data. Many notions of depth have been developed in the last decades. Among others, projection depth appears to be very favorable. It turns out that (Zuo 2003 ; Zuo, Cui, and He 2004; Zuo 2006), with appropriate choices of univariate location and scale estimators, the projection depth induced estimators usually possess very high breakdown point robustness and infinite sample relative efficiency. However, the computation of the projection depth seems hopeless and intimidating if not impossible. This hinders the further inference procedures development in practice. Sporadically algorithms exist in individual papers, though an unified computation package for projection depth has not been documented. To fill the gap, a MATLAB package entitled CompPD is presented in this paper, which is in fact an implementation of the latest developments (Liu, Zuo, and Wang 2013; Liu and Zuo 2014). Illustrative examples are also provided to guide readers through step-by-step usage of package CompPD to demonstrate its utility.