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Contrast function estimation for the drift parameter of ergodic jump diffusion process
Author(s) -
Amorino Chiara,
Gloter Arnaud
Publication year - 2020
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.12406
Subject(s) - mathematics , discretization , jump , contrast (vision) , ergodic theory , jump process , estimator , jump diffusion , function (biology) , diffusion process , diffusion , process (computing) , mathematical analysis , statistical physics , statistics , computer science , physics , knowledge management , innovation diffusion , quantum mechanics , artificial intelligence , evolutionary biology , biology , thermodynamics , operating system
Abstract In this paper, we consider an ergodic diffusion process with jumps whose drift coefficient depends on an unknown parameter. We suppose that the process is discretely observed. We introduce an estimator based on a contrast function, which is efficient without requiring any conditions on the rate at which the step discretization goes to zero, and where we allow the observed process to have nonsummable jumps. This extends earlier results where the condition on the step discretization was needed and where the process was supposed to have summable jumps. In general situations, our contrast function is not explicit and one has to resort to some approximation. In the case of a finite jump activity, we propose explicit approximations of the contrast function such that the efficient estimation of the drift parameter is feasible. This extends the results obtained by Kessler in the case of continuous processes.