Half-region depth for stochastic processes

James Kuelbs and Joel Zinn

Journal of Multivariate Analysis, 2015, vol. 142, issue C, 86-105

Abstract: We study the concept of half-region depth, introduced in López-Pintado and Romo (2011). We show that for a wide variety of standard stochastic processes, such as Brownian motion and other symmetric stable processes with stationary independent increments tied down at 0, half-region depth assigns depth zero to all sample functions. To alleviate this difficulty we introduce a method of smoothing, which often not only eliminates the problem of zero depth, but allows us to extend the theoretical results on consistency in that paper up to the n level for many smoothed processes.

Keywords: Depth; Consistency; Central limit theorems; Empirical processes (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1016/j.jmva.2015.07.012

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