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Asymptotic expansions and bootstrapping distributions for dependent variables: A martingale approach. (English) Zbl 0759.62011
Author’s abstract: The paper develops a one-step triangular array asymptotic expansion for continuous martingales which are asymptotically normal. Mixing conditions are not required, but the quadratic variations of the martingales must satisfy a law of large numbers and a central limit type condition. From this result, we derive expansions for the distributions of estimators in asymptotically ergodic differential equation models, and also for the bootstrapping estimators of these distributions.

MSC:
62E20 Asymptotic distribution theory in statistics
62M05 Markov processes: estimation; hidden Markov models
60F99 Limit theorems in probability theory
62M09 Non-Markovian processes: estimation
60F05 Central limit and other weak theorems
60G44 Martingales with continuous parameter
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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