MARTINGALE ESTIMATING FUNCTIONS BASED ON EIGENFUNCTIONS FOR DISCRETELY OBSERVED SMALL DIFFUSIONS
Masayuki Uchida · Bulletin of informatics and cybernetics · 2006
We consider asymptotic properties of an estimator of a drift parameter for a one-dimensional diffusion process with small dispersion parameter $ \\varepsilon $. For discrete data observed at equidistant times $ k/n, k=0, 1, ldots, n,$ we study consistency and asymptotic normality of an M-estimator derived from a martingale estimating function based on an eigenfunction as $ \\varepsilon $ tends to $ 0 $ and $ n $ tends to $ infty $ simultaneously.