Diffusions with measurement errors. II. Optimal estimators
ESAIM: Probability and Statistics, Volume 5 (2001), pp. 243-260

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 ρ n . 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.

Classification: 60J60, 62F12, 62M05
Keywords: statistics of diffusions, measurement errors, LAN property 
@article{PS_2001__5__243_0,
     author = {Gloter, Arnaud and Jacod, Jean},
     title = {Diffusions with measurement errors. {II.} {Optimal} estimators},
     journal = {ESAIM: Probability and Statistics},
     pages = {243--260},
     publisher = {EDP Sciences},
     volume = {5},
     year = {2001},
     mrnumber = {1875673},
     zbl = {1009.60065},
     language = {en},
     url = {https://www.numdam.org/item/PS_2001__5__243_0/}
}
TY  - JOUR
AU  - Gloter, Arnaud
AU  - Jacod, Jean
TI  - Diffusions with measurement errors. II. Optimal estimators
JO  - ESAIM: Probability and Statistics
PY  - 2001
SP  - 243
EP  - 260
VL  - 5
PB  - EDP Sciences
UR  - https://www.numdam.org/item/PS_2001__5__243_0/
LA  - en
ID  - PS_2001__5__243_0
ER  - 
%0 Journal Article
%A Gloter, Arnaud
%A Jacod, Jean
%T Diffusions with measurement errors. II. Optimal estimators
%J ESAIM: Probability and Statistics
%D 2001
%P 243-260
%V 5
%I EDP Sciences
%U https://www.numdam.org/item/PS_2001__5__243_0/
%G en
%F PS_2001__5__243_0
Gloter, Arnaud; Jacod, Jean. Diffusions with measurement errors. II. Optimal estimators. ESAIM: Probability and Statistics, Volume 5 (2001), pp. 243-260. https://www.numdam.org/item/PS_2001__5__243_0/

[1] G. Dohnal, On estimating the diffusion coefficient. J. Appl. Probab. 24 (1987) 105-114. | Zbl | MR

[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. | Zbl | Numdam

[3] A. Gloter and J. Jacod, Diffusion with measurement error. I. Local Asymptotic Normality (2000). | Zbl | MR | Numdam

[4] J. Jacod and A. Shiryaev, Limit Theorems for Stochastic Processes. Springer-Verlag, Berlin (1987). | Zbl | MR

[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. | Zbl | MR | Numdam

[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. Sankyā Ser. A 25 (1963) 293-302. | Zbl | MR