Regression Depth for Statistical Depth Function

Abstract

The statistical depth function is one of the modern approaches that can be used for developing multivariate robust regression based on robust estimates of the location and dispersion matrix. One merit advantage of the depth concept is that it can be used directly to provide deeper estimation functions for data location and regression parameters in a multidimensional environment. The deeper estimation functions induced by depth are expected to inherit the desired and inherent robustness properties (such as limited maximum bias, impact function, and high breaking point) as do their counterparts at univariate sites. Investigation. The main objective of this article is to check the power of the statistical depth function throw the depth regression, it turns out that the deepest functional projection possesses a finite effect function and the best possible asymptotic breakpoint as well as the best breaking point of a finite sample compared with some classical and robust existed method.