Adaptive Exponential Power Depth with Application to Classification

Yunlu Jiang, Canhong Wen and Xueqin Wang ()
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Yunlu Jiang: Jinan University
Canhong Wen: Sun Yat-Sen University
Xueqin Wang: Sun Yat-Sen University

Journal of Classification, 2018, vol. 35, issue 3, No 5, 466-480

Abstract: Abstract 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.

Keywords: Classification; Exponential power depth; Statistical depth function (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s00357-018-9264-z

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