Diffusions with measurement errors. II. Optimal estimators

Arnaud Gloter; Jean Jacod

ESAIM: Probability and Statistics (2001)

  • 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 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.

How to cite

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Gloter, Arnaud, and Jacod, Jean. "Diffusions with measurement errors. II. Optimal estimators." ESAIM: Probability and Statistics 5 (2001): 243-260. <http://eudml.org/doc/104276>.

@article{Gloter2001,
abstract = {We consider a diffusion process $X$ which is observed at times $i/n$ for $i=0,1,\ldots ,n$, each observation being subject to a measurement error. All errors are independent and centered gaussian with known variance $\rho _n$. 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.},
author = {Gloter, Arnaud, Jacod, Jean},
journal = {ESAIM: Probability and Statistics},
keywords = {statistics of diffusions; measurement errors; LAN property},
language = {eng},
pages = {243-260},
publisher = {EDP-Sciences},
title = {Diffusions with measurement errors. II. Optimal estimators},
url = {http://eudml.org/doc/104276},
volume = {5},
year = {2001},
}

TY - JOUR
AU - Gloter, Arnaud
AU - Jacod, Jean
TI - Diffusions with measurement errors. II. Optimal estimators
JO - ESAIM: Probability and Statistics
PY - 2001
PB - EDP-Sciences
VL - 5
SP - 243
EP - 260
AB - We consider a diffusion process $X$ which is observed at times $i/n$ for $i=0,1,\ldots ,n$, each observation being subject to a measurement error. All errors are independent and centered gaussian with known variance $\rho _n$. 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.
LA - eng
KW - statistics of diffusions; measurement errors; LAN property
UR - http://eudml.org/doc/104276
ER -

References

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  1. [1] G. Dohnal, On estimating the diffusion coefficient. J. Appl. Probab. 24 (1987) 105-114. Zbl0615.62109MR876173
  2. [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. Zbl0770.62070
  3. [3] A. Gloter and J. Jacod, Diffusion with measurement error. I. Local Asymptotic Normality (2000). Zbl1008.60089MR1875672
  4. [4] J. Jacod and A. Shiryaev, Limit Theorems for Stochastic Processes. Springer-Verlag, Berlin (1987). Zbl0635.60021MR959133
  5. [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. Zbl0884.60038MR1478732
  6. [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. [7] A. Renyi, On stable sequences of events. Sankyā Ser. A 25 (1963) 293-302. Zbl0141.16401MR170385

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