Minimum Hellinger distance estimation for bivariate samples and time series with applications to nonlinear regression and copula-based models

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• 作者：Annabel Prause ; Ansgar Steland ; Mohammed Abujarad
• 关键词：ARCH ; Central limit theorem ; Change point ; Copulas ; Density estimation ; Nonparametric ; Mixing ; Time series
• 刊名：Metrika
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：79
• 期：4
• 页码：425-455
• 全文大小：603 KB
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• 作者单位：Annabel Prause (1)
  Ansgar Steland (1)
  Mohammed Abujarad (1)
  
  1. Institute of Statistics, RWTH Aachen University, Wüllnerstr. 3, 52062, Aachen, Germany
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics
  Statistics
  Statistics for Business, Economics, Mathematical Finance and Insurance
  Probability Theory and Stochastic Processes
  Economic Theory
  
• 出版者：Physica Verlag, An Imprint of Springer-Verlag GmbH
• ISSN：1435-926X

文摘

We study minimum Hellinger distance estimation (MHDE) based on kernel density estimators for bivariate time series, such that various commonly used regression models and parametric time series such as nonlinear regressions with conditionally heteroscedastic errors and copula-based Markov processes, where copula densities are used to model the conditional densities, can be treated. It is shown that consistency and asymptotic normality of the MHDE basically follow from the uniform consistency of the density estimate and the validity of the central limit theorem for its integrated version. We also provide explicit sufficient conditions both for the i.i.d. case and the case of strong mixing series. In addition, for the case of i.i.d. data, we briefly discuss the asymptotics under local alternatives and relate the results to maximum likelihood estimation.