We consider a diffusion process which is observed at times for , each observation being subject to a measurement error. All errors are independent and centered gaussian with known variance . 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 is a gaussian martingale, and we conjecture that they are also optimal in the general case.
Mots-clés : 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://archive.numdam.org/item/PS_2001__5__243_0/} }
Gloter, Arnaud; Jacod, Jean. Diffusions with measurement errors. II. Optimal estimators. ESAIM: Probability and Statistics, Tome 5 (2001), pp. 243-260. http://archive.numdam.org/item/PS_2001__5__243_0/
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