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Non‐Parametric Estimation of the Conditional Distribution of the Interjumping Times for Piecewise‐Deterministic Markov Processes
Author(s) -
Azaïs Romain,
Dufour François,
GégoutPetit Anne
Publication year - 2014
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12076
Subject(s) - mathematics , estimator , piecewise , conditional probability distribution , consistency (knowledge bases) , generalization , multiplicative function , strong consistency , markov process , interval (graph theory) , parametric statistics , statistics , discrete mathematics , combinatorics , mathematical analysis
This paper presents a non‐parametric method for estimating the conditional density associated to the jump rate of a piecewise‐deterministic Markov process. In our framework, the estimation needs only one observation of the process within a long time interval. Our method relies on a generalization of Aalen's multiplicative intensity model. We prove the uniform consistency of our estimator, under some reasonable assumptions related to the primitive characteristics of the process. A simulation study illustrates the behaviour of our estimator.