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Delay Estimation for Some Stationary Diffusion‐type Processes
Author(s) -
Kuchler Uwe,
Kutoyants Y. A.
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 - 10.1111/1467-9469.00197
Subject(s) - mathematics , estimator , stochastic differential equation , term (time) , diffusion , limit (mathematics) , diffusion process , type (biology) , bayesian probability , mathematical analysis , statistics , innovation diffusion , ecology , knowledge management , physics , quantum mechanics , biology , computer science , thermodynamics
In this paper the asymptotic behaviour of the maximum likelihood and Bayesian estimators of a delay parameter is studied. The observed process is supposed to be the solution of a linear stochastic differential equation with one time delay term. It is shown that these estimators are consistent and their limit distributions are described. The behaviour of the estimators is similar to the behaviour of corresponding estimators in change‐point problems. The question of asymptotical efficiency is also discussed.