an:01294462
Zbl 0980.62074
Kessler, Mathieu; S??rensen, Michael
Estimating equations based on eigenfunctions for a discretely observed diffusion process
EN
Bernoulli 5, No. 2, 299-314 (1999).
00056021
1999
j
62M05 60J60 60H10 62F12
optimal estimating functions; quasilikelihood; generators
Summary: A new type of martingale estimating functions is proposed for inference about classes of diffusion processes based on discrete-time observations. These estimating functions can be tailored to a particular class of diffusion processes by utilizing a martingale property of the eigenfunctions of the generators of the diffusions.
Optimal estimating functions in the sense of \textit{V.P. Godambe} and \textit{C.C. Heyde} [Int. Stat. Rev. 55, 231-244 (1987; Zbl 0671.62007)] are found. Inference based on these is invariant under transformations of data. A result on consistency and asymptotic normality of the estimators is given for ergodic diffusions. The theory is illustrated by several examples and by a simulation study.
Zbl 0671.62007