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$M$-estimation for discretely sampled diffusions
Jaya P. N. Bishwal Department of Mathematics and Statistics, University of North Carolina at Charlotte, 376 Fretwell Bldg, 9201 University City Blvd., Charlotte, NC 28223-0001
Аннотация:
We study the estimation of a parameter in the nonlinear drift coefficient of a stationary ergodic diffusion process satisfying a homogeneous Itô stochastic differential equation based on discrete observations of the process, when the true model does not necessarily belong to the observer's model. Local asymptotic normality of $M$-ratio random fields are studied. Asymptotic normality of approximate $M$-estimators based on the Itô and Fisk–Stratonovich approximations of a continuous $M$-functional are obtained under a moderately increasing experimental design condition through the weak convergence of approximate $M$-ratio random fields. The derivatives of an approximate log-$M$ functional based on the Itô approximation are martingales, but the derivatives of a log-$M$ functional based on the Fisk–Stratonovich approximation are not martingales, but the average of forward and backward martingales. The averaged forward and backward martingale approximations have a faster rate of convergence than the forward martingale approximations.
Ключевые слова:
Itô stochastic differential equations, diffusion processes, model misspecification, discrete observations, moderately increasing experimental design, approximate $M$-estimators, local asymptotic normality, robustness, weak convergence of random fields.
Образец цитирования:
Jaya P. N. Bishwal, “$M$-estimation for discretely sampled diffusions”, Theory Stoch. Process., 15(31):2 (2009), 62–83
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/thsp86 https://www.mathnet.ru/rus/thsp/v15/i2/p62
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Страница аннотации: | 115 | PDF полного текста: | 35 | Список литературы: | 26 |
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