Maximum-Likelihood Asymptotic Inference for Autoregressive Hilbertian Processes

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• 作者：M. D. Ruiz-Medina (1)
  R. M. Espejo (2)
  
  1. Department of Statistics and Operations Research ; Faculty of Sciences ; University of Granada ; Campus Fuente Nueva s/n ; 18071 ; Granada ; Spain
  2. Faculty of Sciences ; University of Granada ; Campus Fuente Nueva s/n ; 18071 ; Granada ; Spain
  
• 关键词：Autoregressive Hilbertian processes ; Central limit results ; EM聽algorithm ; Financial data ; Maximum likelihood estimation ; Missing functional data ; Numerical projection methods ; 60G42 ; 60G15 ; 62E20 ; 62F12
• 刊名：Methodology and Computing in Applied Probability
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：17
• 期：1
• 页码：207-222
• 全文大小：994 KB
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  3. Bosq D (2000) Linear processes in function spaces. Springer-Verlag
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  15. Ruiz-Medina MD, Salmer贸n R (2011) Asymptotic properties of functional maximum-likelihood ARH parameter estimators. Rev Nouv Technol Inf 33鈥?8 (Special issue of JSFdS Bordeaux 2009)
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• 刊物主题：Statistics, general; Life Sciences, general; Electrical Engineering; Economics general; Business/Management Science, general;
• 出版者：Springer US
• ISSN：1573-7713

文摘

The autoregressive Hilbertian process framework has been introduced in Bosq (2000). This book provides the nonparametric estimation of the autocorrelation and covariance operators of the autoregressive Hilbertian processes. The asymptotic properties of these estimators are also provided. The maximum likelihood approach still remains unexplored. This paper obtains the asymptotic distribution of the maximum likelihood (ML) estimators of the auto-covariance operator of the Hilbert-valued innovation process, and of the autocorrelation operator of a Gaussian autoregressive Hilbertian process of order one. A real data example is analyzed in the financial context for illustration of the performance of the projection maximum likelihood estimation methodology in the context of missing data.