Functional maximum-likelihood estimation of ARH(p) models

Stochastic Environmental Research and Risk Assessment

Volumn 24, Issue 1, 2010, Pages 131-146

  Ruiz Medina, M D ^a   Salmeron R ^a  

^a UNIVERSITY OF GRANADA   (Spain)

Author keywords

Autoregressive Hilbertian models; Dimension reduction; Finite dimensional approximation; Functional parameters; Maximum likelihood estimation; Singular value decomposition; Spatial functional data sequence

Indexed keywords

AUTO-REGRESSIVE; AUTOREGRESSIVE HILBERTIAN MODELS; DIMENSION REDUCTION; FINITE-DIMENSIONAL APPROXIMATION; FUNCTIONAL DATAS; FUNCTIONAL PARAMETERS;

ALGORITHMS; HELICOPTER CRANES; PARAMETER ESTIMATION; SECURITY OF DATA; SINGULAR VALUE DECOMPOSITION;

MAXIMUM LIKELIHOOD ESTIMATION;

ALGORITHM; ESTIMATION METHOD; FOURIER TRANSFORM; KALMAN FILTER; MAXIMUM LIKELIHOOD ANALYSIS;

EID: 77949773871     PISSN: 14363240     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00477-009-0306-2     Document Type: Article

References (49)

1. Alter O (2000) Singular value decomposition for genome-wide expression data processing and modelling. Proc Natl Acad Sci 97: 10101-10106 (Online).
2. Alter O, Golub GH (2003) Generalized singular value decomposition for comparative analysis of genome-scale expression data sets of two different organisms. Proc Natl Acad Sci 100: 3351-3356 (Online).
3. Antoniadis A, Sapatinas T (2003) Wavelet methods for continuous-time prediction using Hilbert-valued autoregressive processes. J Multivar Anal 87: 133-158.
4. Bar-Joseph Z, Gerber G, Jaakkola T, Gifford D, Simon I (2003) Continuous representation of time-series gene expression data. J Comput Biol 10: 341-356.
5. Bar-Joseph Z (2004) Analyzing time series gene expression data. Bioinformatics 20: 2493-503.
6. Besse P, Cardot H, Stephenson DB (2000) Autoregressive forecasting of some functional climatic variations. Scand J Stat 27: 673-687.
7. Bosq D (1991) Nonparametric statistics for stochastic processes, estimation and prediction. Lectures Notes in Statistics, vol 110. Springer, New York.
8. Bosq D (2000) Linear processes in function spaces. Springer, New York.
9. Bosq D (2008) A note on asymptotic parametric prediction. J Stat Plann Infer. doi:10.1016/j.jspi.2008.07.018.
10. Bosq D, Blanke D (2007) Inference and prediction in large dimensions, Wiley Series in Probability and Statistics. Wiley, New York.
11. Cardot H (1997) Contribution á l'estimation et á la prévision statistique de doneées fonctionnelles. Ph. D. thesis, University of Toulouse 3, France.
12. Cavanaugh JE (1997) Unifying the derivation for the Akaike and corrected Akaike criteria. Stat Prob Lett 33: 202-208.
13. Christakos G (1985) Recursive parameter estimation with applications in Earth sciences. Math Geol 17: 489-515.
14. Christakos G (1988) On-line estimation of nonlinear physical systems. Math Geol 20: 111-133.
15. Christakos G (2005) Random field models in earth sciences. Academic Press, San Diego.
16. Christakos G, Hristopulos DT (1998) Spatiotemporal environmental health modelling. Kluwer, Boston.
17. Damon J, Guillas S (2005) Estimation and simulation of autoregressive hilbertian processes with exogenous variables. Stat Infer Stoch Proc 8: 185-204.
18. Dautray R, Lions JL (1992) Mathematical analysis and numerical methods for science and technology 3. Spectral theory and applications. Springer, Berlin.
19. Dunford N, Schwartz JT (1971) Linear operators, part iii, spectral operators. Wiley, New York Interscience.
20. Ferraty F, Vieu P (2006) Nonparameric functional data analysis, Springer series in statistics. Springer, New York.
21. Germain F, Doisy A, Ronot X, Tracqui P (1999) Characterization of cell deformation and migration using a parametric estimation of image motion. IEEE Trans Biomed Eng 46: 584-600.
22. Goia A (2003) Selection model in functional linear regression models for scalar response. In: Ferligoj A, Mrvar A (eds) Developments in Applied Statistics, Metodoloski zvezki, vol 19, FDV, Ljubljana.
23. Guillas S (2001) Rates of convergence of autocorrelation estimates for autoregressive Hilbertian processes. Stat Prob Lett 55: 281-291.
24. Hall P, Poskitt DS, Presnell B (2001) A functional data-analytic approach to signal discrimination. Technometrics 43: 1-9.
25. Haoudi A, Bensmail H (2006) Bioinformatics and data mining in proteomics. Expert Rev Proteomics 3: 333-343.
26. Kato T (1995) Perturbation theory of linear operators. Springer, New York.
27. Klevezc RR, Murray DB (2001) Genome wide oscillations in expression: wavelet analysis of time series data from yest expression arrays uncovers the dynamic architecture of phenotype. Mol Biol Rep 28: 73-82.
28. Leng X, Müller H-G (2006) Classification using functional data analysis for temporal gene expression data. Bioinformatics 22: 68-76.
29. Mas A (1999) Normalité asymptotique de l'estimateur empirique de l'opérateur d'autocorrélation d'un processus ARH(1). C R Acad Sci Paris, 329 Série I, pp 899-902.
30. Mas A (2007) Weak convergence in the functional autoregressive model. J Multivar Anal 98: 1231-1261.
31. Matheron G, Traité de géoestatistique apliquée, tome I, mémoires du Bureau de Recherches Géologiques et Miniéres, Editions Bureau de Recherches Geologiques et Miniéres, Paris, 24, 1962.
32. Merlévede F (1996) Processus linéaires Hilbertiens: inversibilité, theorémes limites, estimation et prévision, Ph. D. Thesis, University of París 6, France.
33. Monk NAM (2003) Unravelling nature's networks. Biochem Soc Trans 31: 1457-1561.
34. Mourid T (1995) Contribution á la statistique des processus autiregréssifs á temps continu. Ph. D. thesis, University of Paris 6, France.
35. Mourid T, Bensmain N (2006) Sieves estimator of the operator of a functional autoregressive process. Stat Prob Lett 76: 93-108.
36. Müller HG (2005) Functional modelling and classification of longitudinal data. Scand J Statist 32: 223-240.
37. Müller HG, Stadmüller U (2005) Generalized functional models. Ann Stat 33: 774-885.
38. Pumo B (1992) Estimation et prévision de processus autirégressifs fonctionnels. Application aux processus á temps continu. Ph. D. thesis, University of París 6, France.
39. Ramsay JO, Silverman BW (2005) Functional data analysis, Springer series in statistics. Springer, New York.
40. Raychadhuri S, Stuart JM, Altman RB (2000) Principal component analysis to summarize microarray experiments: application to sporulation time series. Pacif Sympos Bicomp 5: 452-63.
41. Ruiz-Medina MD, Salmerón R, Angulo JM (2007) Kalman filtering from POP-based diagonalization of ARH(1). Comput Stat Data Anal 51: 4994-5008.
42. Salmerón R, Ruiz-Medina MD (2009a) Multispectral decomposition of FAR(p) models. Stoch Env Res Risk Assess 23: 289-297.
43. Salmerón R, Ruiz-Medina MD (2009b) Functional SEM algorithm in ARH(1) models. XXXI Congreso Nacional de Estadística e Investigación Operativa, Spain.
44. Schwartz G (1978) Estimating the dimension of a model. Ann Stat 6: 461-464.
45. Shibata R (1981) An optimal selection of regression variables. Biometrika 68: 45-54.
46. Song JJ, Lee H-J, Morris JS, Kangd S (2007) Clustering of time-course gene expression data using fuctional data analysis. Comput Biol Chem 31: 265-274.
47. Vieu P (1995) Order choice in nonlinear autoregressive models. Statistics 26: 307-328.
48. Yao F, Müller HG, Clifford AJ, Dueker SR, Lin Follett J, Buchholz BAY, Vogel JS (2003) Shrinkage estimation for functional principal component scores with application to the population kinetics of plasma folate. Biometrics 59: 676-685.
49. Yao F, Müller HG, Wang JL (2005) Functional data analysis for sparse longitudinal data. J Am Stat Assoc100: 577-590.