Premium
Simple and Explicit Estimating Functions for a Discretely Observed Diffusion Process
Author(s) -
Kessler Mathieu
Publication year - 2000
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 - 10.1111/1467-9469.00179
Subject(s) - mathematics , ergodic theory , estimator , equidistant , diffusion process , discretization , diffusion , simple (philosophy) , mathematical analysis , statistics , geometry , knowledge management , physics , innovation diffusion , philosophy , epistemology , computer science , thermodynamics
We consider a one‐dimensional diffusion process X , with ergodic property, with drift b ( x , θ) and diffusion coefficient a ( x , θ) depending on an unknown parameter θ that may be multidimensional. We are interested in the estimation of θ and dispose, for that purpose, of a discretized trajectory, observed at n equidistant times t i = iΔ , i = 0, ..., n . We study a particular class of estimating functions of the form ∑ f (θ, X t i −1 ) which, under the assumption that the integral of f with respect to the invariant measure is null, provide us with a consistent and asymptotically normal estimator. We determine the choice of f that yields the estimator with minimum asymptotic variance within the class and indicate how to construct explicit estimating functions based on the generator of the diffusion. Finally the theoretical study is completed with simulations.