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Nonparametric Estimation for a Class of Piecewise-Deterministic Markov Processes

  • Takayuki Fujii (a1)

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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Copyright

Corresponding author

Current address: Faculty of Economics, Shiga University, 1-1-1 Banba, Hikone, Shiga 522-8522, Japan. Email address: takayuki-fujii@biwako.shiga-u.ac.jp

References

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Nonparametric Estimation for a Class of Piecewise-Deterministic Markov Processes

  • Takayuki Fujii (a1)

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