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Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 1998-27
November 1998

Discretely observed diffusions: classes of estimating functions and small $Delta$-optimality


Martin Jacobsen


Ergodic diffusions in several dimensions, depending on an unknown multivariate parameter are considered. For estimation, when the diffusion is observed only at finitely many equidistant timepoints, unbiased estimating functions leading to consistent and asymptotically Gaussian estimators are used. Different types of estimating functions are discussed and the concept of small $Delta -$optimality is introduced to help select good estimating functions. Explicit criteria for small $Delta -$optimality are given. Also some exact optimality conditions are presented as well as, for one-dimensional diffusions, methods for improving estimators using time reversibility.

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This paper has now been published in Scand. J. Statist. 28, 123-149 (2001)