Estimating functions for noisy observations of ergodic diffusions

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• 作者：Benjamin Favetto
• 关键词：Estimating functions ; Diffusion process ; Parametric inference ; Discrete time noisy observations ; Central limit theorem
• 刊名：Statistical Inference for Stochastic Processes
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：19
• 期：1
• 页码：1-28
• 全文大小：583 KB
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• 作者单位：Benjamin Favetto (1)
  
  1. Université Paris Descartes, 45, rue des Saints Péres, 75006, Paris, France
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Probability Theory and Stochastic Processes
  
• 出版者：Springer Netherlands
• ISSN：1572-9311

文摘

In this article, general estimating functions for ergodic diffusions sampled at high frequency with noisy observations are presented. The theory is formulated in terms of approximate martingale estimating functions based on local means of the observations, and simple conditions are given for rate optimality. The estimation of the diffusion parameter is faster than the estimation of the drift parameter, and the rate of convergence is classical for the drift parameter but not classical for the diffusion parameter. The link with specific minimum contrast estimators is established, as an example.