Discretely Observed Diffusions: Classes of Estimating Functions and Small Δ‐optimality

Abstract

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 time points, unbiased estimating functions leading to consistent and asymptotically Gaussian estimators are used. Different types of estimating functions are discussed and the concept of small Δ‐optimality is introduced to help select good estimating functions. Explicit criteria for small Δ‐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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