Maximum-Likelihood Asymptotic Inference for Autoregressive Hilbertian Processes
详细信息 查看全文
- 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
- 参考文献：1. Aalen OO, Gunnes N (2010) A dynamic approach for reconstructing missing longitudinal data using the linear increments model. Biostatistics 11:453鈥?72 external" href="http://dx.doi.org/10.1093/biostatistics/kxq014" target="_blank" title="It opens in new window">CrossRef
2. Basse M, Diop A, Dabo-Niang S (2008) Mean square properties of a class of kernel density estimates for spatial functional random variables. In: Annales De L鈥橧.S.U.P. Publications de l鈥橧nstitut de Statistique de l鈥橴niversit茅 de Paris. Num茅ro Sp茅cial-Volume LII. Fascicule 1鈥?, Paris, pp 91鈥?08
3. Bosq D (2000) Linear processes in function spaces. Springer-Verlag
4. Bosq D, Blanke D (2007) Inference and predictions in large dimensions. Wiley, New York external" href="http://dx.doi.org/10.1002/9780470724033" target="_blank" title="It opens in new window">CrossRef
5. Da Prato G, Zabczyk J (2002) Second order partial differential equations in Hilbert spaces. Cambridge University Press, New York external" href="http://dx.doi.org/10.1017/CBO9780511543210" target="_blank" title="It opens in new window">CrossRef
6. Dautray R, Lions J-L- (1985) Mathematical analysis and numerical methods for science and technology, vol聽3: spectral theory and applications. Springer. ISBN 978-3-540-66099-6 (2nd printing, 2000, X, p 542)
7. Ferraty F, Vieu P (2006) Nonparameric functional data analysis. Springer, New York
8. Guillas S, Lai M-J (2010) Bivariate splines for spatial functional regression models. J Nonparametr Stat 22:477鈥?97 external" href="http://dx.doi.org/10.1080/10485250903323180" target="_blank" title="It opens in new window">CrossRef
9. H枚rmann S, Kokoszka P (2010) Weakly dependent functional data. Ann Stat 38:1845鈥?884 external" href="http://dx.doi.org/10.1214/09-AOS768" target="_blank" title="It opens in new window">CrossRef
10. Nakai M, Ke W (2011) Review of methods for handling missing data in longitudinal data analysis. Int J Math Anal 5:1鈥?3
11. Ramsay J, Silverman B (2005) Functional data analysis. Springer, New York
12. Ruiz-Medina MD (2011) Spatial autoregressive and moving average Hilbertian processes. J Multivar Anal 102:292鈥?05 external" href="http://dx.doi.org/10.1016/j.jmva.2010.09.005" target="_blank" title="It opens in new window">CrossRef
13. Ruiz-Medina MD (2012) Spatial functional prediction from spatial autoregressive Hilbertian processes. Environmetrics 23:119鈥?28 external" href="http://dx.doi.org/10.1002/env.1143" target="_blank" title="It opens in new window">CrossRef
14. Ruiz-Medina MD, Salmer贸n R (2010) Functional maximum-likelihood estimation of ARH(p) models. Stoch Environ Res Risk Assess 24:131鈥?46 external" href="http://dx.doi.org/10.1007/s00477-009-0306-2" target="_blank" title="It opens in new window">CrossRef
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)
16. Salmer贸n R, Ruiz-Medina MD (2009) Multispectral decomposition of functional autoregressive models. Stoch Environ Res Risk Assess 23:289鈥?97 external" href="http://dx.doi.org/10.1007/s00477-008-0213-y" target="_blank" title="It opens in new window">CrossRef
17. Walk H (1977) An invariance principle for the Robbins鈥揗onro process in a Hilbert space. Z Wahrscheinlichkeitstheor Verw Geb 39:135鈥?50 external" href="http://dx.doi.org/10.1007/BF00535182" target="_blank" title="It opens in new window">CrossRef - 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.