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

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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.

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 = {http://geodesic.mathdoc.fr/item/PS_2001__5__243_0/}
}
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Gloter, Arnaud; Jacod, Jean. Diffusions with measurement errors. II. Optimal estimators. ESAIM: Probability and Statistics, Tome 5 (2001), pp. 243-260. http://geodesic.mathdoc.fr/item/PS_2001__5__243_0/