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Constructing fixed rank optimal estimators with method of best recurrent approximations

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  • Torokhti, Anatoli
  • Howlett, Phil

Abstract

We propose a new approach which generalizes and improves principal component analysis (PCA) and its recent advances. The approach is based on the following underlying ideas. PCA can be reformulated as a technique which provides the best linear estimator of the fixed rank for random vectors. By the proposed method, the vector estimate is presented in a special quadratic form aimed to improve the error of estimation compared with customary linear estimates. The vector is first pre-estimated from the special iterative procedure such that each iterative loop consists of a solution of the unconstrained nonlinear best approximation problem. Then, the final vector estimate is obtained from a solution of the constrained best approximation problem with the quadratic approximant. We show that the combination of these techniques allows us to provide a new nonlinear estimator with a significantly better performance compared with that of PCA and its known modifications.

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  • Torokhti, Anatoli & Howlett, Phil, 2003. "Constructing fixed rank optimal estimators with method of best recurrent approximations," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 293-309, August.
    • Handle: RePEc:eee:jmvana:v:86:y:2003:i:2:p:293-309
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    References listed on IDEAS

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    1. Ocaña, F. A. & Aguilera, A. M. & Valderrama, M. J., 1999. "Functional Principal Components Analysis by Choice of Norm," Journal of Multivariate Analysis, Elsevier, vol. 71(2), pages 262-276, November.
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    Cited by:

    1. Howlett, P.G. & Torokhti, A. & Pearce, C.E.M., 2007. "Optimal multilinear estimation of a random vector under constraints of causality and limited memory," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 869-878, October.
    2. Torokhti, Anatoli & Friedland, Shmuel, 2009. "Towards theory of generic Principal Component Analysis," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 661-669, April.

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