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Computational Aspects Related to Martingale Estimating Functions for a Discretely Observed Diffusion
Author(s) -
KESSLER MATHIEU,
PAREDES SILVESTRE
Publication year - 2002
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 - 10.1111/1467-9469.00299
Subject(s) - mathematics , estimator , martingale (probability theory) , monte carlo method , ergodic theory , martingale difference sequence , local martingale , conditional expectation , statistical physics , econometrics , mathematical analysis , statistics , physics
Martingale estimating functions for a discretely observed diffusion have turned out to provide estimators with nice asymptotic properties. However, their expression usually involves some conditional expectation that has to be evaluated through Monte Carlo simulations giving rise to an approximated estimator. In this work we study, for ergodic models, the asymptotic properties of the approximated estimator and describe the influence of the number of independent simulated trajectories involved in the Monte Carlo method as well as of the approximation scheme used. Our results are of practical relevance to assess the implementation of martingale estimating functions for discretely observed diffusions.