Abstract
We investigate the moment estimation for an ergodic diffusion process with unknown trend coefficient. We consider nonparametric and parametric estimation. In each case, we present a lower bound for the risk and then construct an asymptotically efficient estimator of the moment type functional or of a parameter which has a one-to-one correspondence to such a functional. Next, we clarify a higher order property of the moment type estimator by the Edgeworth expansion of the distribution function.
Citation
Yury A. Kutoyants. Nakahiro Yoshida. "Moment estimation for ergodic diffusion processes." Bernoulli 13 (4) 933 - 951, November 2007. https://doi.org/10.3150/07-BEJ1040
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