TITLE:
Some Properties of a Recursive Procedure for High Dimensional Parameter Estimation in Linear Model with Regularization
AUTHORS:
Hong Son Hoang, Remy Baraille
KEYWORDS:
Linear Model, Regularization, Recursive Algorithm, Non-Negative Covariance Structure, Eigenvalue Decomposition
JOURNAL NAME:
Open Journal of Statistics,
Vol.4 No.11,
December
31,
2014
ABSTRACT: Theoretical results related to properties of a regularized recursive algorithm for estimation of a high dimensional vector of parameters are presented and proved. The recursive character of the procedure is proposed to overcome the difficulties with high dimension of the observation vector in computation of a statistical regularized estimator. As to deal with high dimension of the vector of unknown parameters, the regularization is introduced by specifying a priori non-negative covariance structure for the vector of estimated parameters. Numerical example with Monte-Carlo simulation for a low-dimensional system as well as the state/parameter estimation in a very high dimensional oceanic model is presented to demonstrate the efficiency of the proposed approach.