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December 2013 Nonparametric estimation for a class of piecewise-deterministic Markov processes
Takayuki Fujii
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J. Appl. Probab. 50(4): 931-942 (December 2013). DOI: 10.1239/jap/1389370091

Abstract

In this paper we study nonparametric estimation problems for a class of piecewise-deterministic Markov processes (PDMPs). Borovkov and Last (2008) proved a version of Rice's formula for PDMPs, which explains the relation between the stationary density and the level crossing intensity. From a statistical point of view, their result suggests a methodology for estimating the stationary density from observations of a sample path of PDMPs. First, we introduce the local time related to the level crossings and construct the local-time estimator for the stationary density, which is unbiased and uniformly consistent. Secondly, we investigate other estimation problems for the jump intensity and the conditional jump size distribution.

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Takayuki Fujii. "Nonparametric estimation for a class of piecewise-deterministic Markov processes." J. Appl. Probab. 50 (4) 931 - 942, December 2013. https://doi.org/10.1239/jap/1389370091

Information

Published: December 2013
First available in Project Euclid: 10 January 2014

zbMATH: 06279819
MathSciNet: MR3161365
Digital Object Identifier: 10.1239/jap/1389370091

Subjects:
Primary: 62G20
Secondary: 60J55

Rights: Copyright © 2013 Applied Probability Trust

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Vol.50 • No. 4 • December 2013
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