Optimal multilinear estimation of a random vector under constraints of causality and limited memory

Computational Statistics and Data Analysis

Volumn 52, Issue 2, 2007, Pages 869-878

  Howlett, P G ^a   Torokhti, A ^a   Pearce, C E M ^b  

^a UNIVERSITY OF SOUTH AUSTRALIA   (Australia)

^b UNIVERSITY OF ADELAIDE   (Australia)

Author keywords

Causality; Finite memory; Least squares singular pivot algorithm; Multilinear estimation; Random vectors

Indexed keywords

ALGORITHMS; CONSTRAINT THEORY; DATA STORAGE EQUIPMENT; NONLINEAR ANALYSIS; NUMERICAL ANALYSIS;

CAUSALITY; COVARIANCE MATRICES; FINITE MEMORY; LEAST SQUARES SINGULAR PIVOT ALGORITHM; NONLINEAR ESTIMATORS; RANDOM VECTORS;

VECTORS;

EID: 35148867799     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2006.10.020     Document Type: Article

References (31)

1. Ben-Israel A., and Greville T.N.E. Generalized Inverses: Theory and Applications (1974), Wiley, New York
2. Champion C.J. Empirical Bayesian estimation of normal variances and covariances. J. Multivariate Anal. 87 (2003) 60-79
3. Fomin V.N., and Ruzhansky M.V. Abstract optimal linear filtering. SIAM J. Control Optim. 38 (2000) 1334-1352
4. Fukunaga K. Introduction to Statistical Pattern Recognition (1990), Academic Press, Boston
5. Gimeno V. Obtaining the EEG envelope in real time: a practical method based on homomorphic filtering. Neuropsychobiology 18 (1987) 110-112
6. Golub G.H., and van Loan C.F. Matrix Computations (1996), Johns Hopkins University Press, Baltimore
7. Howlett P., Pearce C., and Torokhti A. On problems of best approximation for nonlinear operators. Nonlinear Funct. Anal. Appl. 6 (2001) 351-368
8. Howlett P.G., Torokhti A.P., and Pearce C.E.M. The modelling and numerical simulation of causal non-linear systems. Nonlinear Anal. Theory, Methods Appl. 47 8 (2001) 5559-5572
9. Howlett P.G., Pearce C.E.M., and Torokhti A. An optimal linear filter for random signals with realisations in Hilbert space. ANZIAM J. 44 (2003) 485-500
10. Hua Y., and Liu W.Q. Generalized Karhunen-Loève transform. IEEE Signal Process Lett. 5 6 (1998) 141-143
11. Huet, S., Bouvier, A., Poursat, M.-A., Jolivet, E., 2003. Statistical Tools for Nonlinear Regression. A Practical Guide with S-PLUS and R Examples. Springer Series in Statistics. Springer, Berlin.
12. Kauermann G., and Carroll R.J. A note on the efficiency of sandwich covariance matrix estimation. J. Amer. Statist. Assoc. 96 (2001) 1387-1396
13. Kubokawa T., and Srivastava M.S. Estimating the covariance matrix: a new approach. J. Multivariate Anal. 86 (2003) 28-47
14. Ledoit O., and Wolf M. A well-conditioned estimator for large-dimensional covariance matrices. J. Multivariate Anal. 88 (2004) 365-411
15. Lin Q., and Allebach J.P. Combating speckle in SAR images: vector filtering and sequential classification based on a multiplicative noise model. IEEE Trans. Geoscience Remote Sensing 28 (1990) 647-653
16. Mathews V.J., and Sicuranza G.L. Polynomial Signal Processing (2001), Wiley, New York
17. Moore, A.W., Schneider, J., Deng, K., 1997. Efficient locally weighted polynomial regression predictions. Proceedings of the 14th International Conference on Machine Learning, pp. 236-244.
18. Peña D., and Yohai V. A fast procedure for outlier diagnostics in large regression problems. J. Amer. Statist. Assoc. 94 (1999) 434-445
19. Perlovsky L.I., and Marzetta T.L. Estimating a covariance matrix from incomplete realizations of a random vector. IEEE Trans. Signal Process. 40 (1992) 2097-2100
20. Ruzhansky M.V., and Fomin V.N. The optimal filter construction with the quadratic quality functional of general form. Vestnik St. Petersburg Univ. Math. 28 (1996) 42-46
21. Schneider M.K., and Willsky A.S. A Krylov subspace method for covariance approximation and simulation of a random process and fields. Multidimen. Systems Signal Process. 14 (2003) 295-318
22. Seber A.F.G., and Wild C.J. Nonlinear Regression (2003), Wiley, New York
23. Sorenson H.W. Parameter Estimation: Principles and Problems (1980), Marcel Dekker, New York
24. Torokhti A., and Howlett P. An optimal filter of the second order. IEEE Trans. Signal Process. 49 (2001) 1044-1048
25. Torokhti A., and Howlett P. Best approximation of operators in the modelling of nonlinear systems. IEEE Trans. Circuits Systems I Fund. Theory Appl. 49 (2002) 1792-1798
26. Torokhti A., and Howlett P. Constructing fixed rank optimal estimators with method of recurrent best approximations. J. Multivariate Anal. 86 (2003) 293-309
27. Torokhti A., Howlett P., and Pearce C. Optimal mathematical models for nonlinear dynamical systems. Math. Comput. Model. Dyn. Syst. 9 (2003) 327-343
28. Torokhti, A., Howlett, P.G., Pearce, C.E.M., LSSP: a new order-reducing methodology for multiple linear regression, submitted for publication.
29. Wang L. Asymptotics of estimates in constrained nonlinear regression with long-range dependent innovations. Ann. Inst. Statist. Math. 56 (2004) 251-264
30. Wu C.O. Local polynomial regression with selection biased data. Statist. Sinica 10 (2000) 789-817
31. Yamashita Y., and Ogawa H. Relative Karhunen-Loève transform. IEEE Trans. Signal Process. 44 (1996) 371-378