Introduction to statistical pattern recognition (2nd ed.)
Introduction to statistical pattern recognition (2nd ed.)
Abstract Optimal Linear Filtering
SIAM Journal on Control and Optimization
Efficient Locally Weighted Polynomial Regression Predictions
ICML '97 Proceedings of the Fourteenth International Conference on Machine Learning
A Krylov Subspace Method for Covariance Approximation and Simulation of Random Processes and Fields
Multidimensional Systems and Signal Processing
Estimating the covariance matrix: a new approach
Journal of Multivariate Analysis
Constructing fixed rank optimal estimators with method of best recurrent approximations
Journal of Multivariate Analysis
Empirical Bayesian estimation of normal variances and covariances
Journal of Multivariate Analysis
A well-conditioned estimator for large-dimensional covariance matrices
Journal of Multivariate Analysis
Relative Karhunen-Loeve transform
IEEE Transactions on Signal Processing
An optimal filter of the second order
IEEE Transactions on Signal Processing
Estimating a covariance matrix from incomplete realizations of arandom vector
IEEE Transactions on Signal Processing
Editorial: 2nd Special Issue on Statistical Signal Extraction and Filtering
Computational Statistics & Data Analysis
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A new technique is provided for random vector estimation from noisy data under the constraints that the estimator is causal and dependent on at most a finite number p of observations. Nonlinear estimators defined by multilinear operators of degree r are employed, the choice of r allowing a trade-off between the accuracy of the optimal filter and the complexity of the calculations. The techniques utilise an exact correspondence of the nonlinear problem to a corresponding linear one. This is then solved by a new procedure, the least squares singular pivot algorithm, whereby the linear problem can be repeated reduced to smaller structurally similar problems. Invertibility of the relevant covariance matrices is not assumed. Numerical experiments with real data are used to illustrate the efficacy of the new algorithm.