Moment estimation for ergodic diffusion processes

Details Moment estimation for ergodic diffusion processes Moment estimation for ergodic diffusion processes

2007-11-26

arxiv.org/abs/0711.3957v1

Bernoulli 2007, Vol. 13, No. 4, 933-951

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/07-BEJ1040 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statist

Scientific paper

10.3150/07-BEJ1040

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.

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