Diffusions with measurement errors. II. Optimal estimators

Arnaud Gloter; Jean Jacod

ESAIM: Probability and Statistics (2010)

  • Volume: 5, page 243-260
  • ISSN: 1292-8100

Abstract

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We consider a diffusion process X which is observed at times i/n for i = 0,1,...,n, each observation being subject to a measurement error. All errors are independent and centered Gaussian with known variance pn. There is an unknown parameter to estimate within the diffusion coefficient. In this second paper we construct estimators which are asymptotically optimal when the process X is a Gaussian martingale, and we conjecture that they are also optimal in the general case.

How to cite

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Gloter, Arnaud, and Jacod, Jean. "Diffusions with measurement errors. II. Optimal estimators." ESAIM: Probability and Statistics 5 (2010): 243-260. <http://eudml.org/doc/197760>.

@article{Gloter2010,
abstract = { We consider a diffusion process X which is observed at times i/n for i = 0,1,...,n, each observation being subject to a measurement error. All errors are independent and centered Gaussian with known variance pn. There is an unknown parameter to estimate within the diffusion coefficient. In this second paper we construct estimators which are asymptotically optimal when the process X is a Gaussian martingale, and we conjecture that they are also optimal in the general case. },
author = {Gloter, Arnaud, Jacod, Jean},
journal = {ESAIM: Probability and Statistics},
keywords = {Statistics of diffusions; measurement errors; LAN property.},
language = {eng},
month = {3},
pages = {243-260},
publisher = {EDP Sciences},
title = {Diffusions with measurement errors. II. Optimal estimators},
url = {http://eudml.org/doc/197760},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Gloter, Arnaud
AU - Jacod, Jean
TI - Diffusions with measurement errors. II. Optimal estimators
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 5
SP - 243
EP - 260
AB - We consider a diffusion process X which is observed at times i/n for i = 0,1,...,n, each observation being subject to a measurement error. All errors are independent and centered Gaussian with known variance pn. There is an unknown parameter to estimate within the diffusion coefficient. In this second paper we construct estimators which are asymptotically optimal when the process X is a Gaussian martingale, and we conjecture that they are also optimal in the general case.
LA - eng
KW - Statistics of diffusions; measurement errors; LAN property.
UR - http://eudml.org/doc/197760
ER -

References

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  1. G. Dohnal, On estimating the diffusion coefficient. J. Appl. Probab.24 (1987) 105-114.  
  2. V. Genon-Catalot and J. Jacod, On the estimation of the diffusion coefficient for multidimensional diffusion processes. Ann. Inst. H. Poincaré Probab. Statist.29 (1993) 119-153.  
  3. A. Gloter and J. Jacod, Diffusion with measurement error. I. Local Asymptotic Normality (2000).  
  4. J. Jacod and A. Shiryaev, Limit Theorems for Stochastic Processes. Springer-Verlag, Berlin (1987).  
  5. J. Jacod, On continuous conditional Gaussian martingales and stable convergence in law, Séminaire Proba. XXXI. Springer-Verlag, Berlin, Lecture Notes in Math. 1655 (1997) 232-246.  
  6. M.B. Malyutov and O. Bayborodin, Fitting diffusion and trend in noise via Mercer expansion, in Proc. 7th Int. Conf. on Analytical and Stochastic Modeling Techniques. Hamburg (2000).  
  7. A. Renyi, On stable sequences of events. Sankya Ser. A25 (1963) 293-302.  

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