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1 results

  • Nonparametric Estimation for a Class of Piecewise-Deterministic Markov Processes

  • Part of
  • Takayuki Fujii
  • Journal:
    Journal of Applied Probability / Volume 50 / Issue 4 / December 2013
    Published online by Cambridge University Press:
    30 January 2018, pp. 931-942
    Print publication:
    December 2013
    • Article
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  • 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.