Nonparametric estimation for a class of piecewise-deterministic markov processes

• Autores: Takayuki Fujii
• Localización: Journal of Applied Probability, ISSN-e 0021-9002, Vol. 50, Nº. 4, 2013, págs. 931-942
• Idioma: inglés
• DOI: 10.1017/s0021900200013711
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• Resumen

  • 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.