Adaptive Exponential Power Depth with Application to Classification.

Depth functions have many applications in multivariate data analysis, including discriminant analysis and classification. In this paper, we introduce a novel class of data depth: exponential power depth (EPD) functions. Under some conditions, we show that the EPD functions are a statistical depth function, and the sample EPD functions are consistent and asymptotically normal. Based on the proposed EPD functions, we construct a DD-plot (depth-versus-depth plot), which can be applied to the classification problem. Since the EPD functions contain the two tuning parameters, we provide a data-driven approach to select these tuning parameters. The simulation studies and two real data analysis are conducted to assess the finite sample performance of the proposed method. [ABSTRACT FROM AUTHOR]