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Estimation for Discretely Observed Small Diffusions Based on Approximate Martingale Estimating Functions
Author(s) -
Uchida Masayuki
Publication year - 2004
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2004.00406.x
Subject(s) - mathematics , martingale (probability theory) , estimator , diffusion process , equidistant , martingale difference sequence , local martingale , statistics , mathematical analysis , geometry , knowledge management , innovation diffusion , computer science
. We consider an asymptotically efficient estimator of the drift parameter for a multi‐dimensional diffusion process with small dispersion parameter ɛ . In the situation where the sample path is observed at equidistant times k / n , k = 0, 1, …, n , we study asymptotic properties of an M ‐estimator derived from an approximate martingale estimating function as ɛ tends to 0 and n tends to ∞ simultaneously.