ASYMPTOTIC EXPANSIONS AND BOOTSTRAPPING DISTRIBUTIONS FOR DEPENDENT-VARIABLES - A MARTINGALE APPROACH

• 成果类型: Article
• 署名作者: MYKLAND, PA
• 署名单位: University of California System; University of California Berkeley
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176348649
• 发表日期: 1992
• 页码: 623-654
• 关键词: maximum-likelihood estimator; central limit-theorems; homogeneous diffusion-processes; confidence-intervals; Edgeworth Expansion; continuous-time; markov-chains; CONVERGENCE; statistics; ratio

摘要

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.