Mathematics > Statistics Theory
[Submitted on 22 Jan 2014]
Title:Half-Region Depth for Stochastic Processes
View PDFAbstract:We study the concept of half-region depth, introduced by Lopez-Pintado and Romo in 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 $\sqrt n$ level for many smoothed processes.
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