R/D optimal linear prediction

Sparse Vector Linear Prediction with Optimal Structures

A modification of a classical Vector Linear Prediction (VLP) technique is proposed in this paper, enabling significant reduction in complexity. The proposed sparse VLP technique (sVLP) is based on predictors with reduced number of nonzero elements. For a given input vector process, a design procedure for obtaining optimal sparse predictor structures and matrix elements is described. The effecti...

Optimal Prediction in Linear Regression Analysis

Expressions are derived for generalized ridge and ordinary ridge predictors that are optimal in terms of mean squared error of prediction (MSEP) for predicting the response at a single or at multiple future observation(s). Using the MSEP criterion, operational predictors are compared to the ordinary least squares (OLS) predictor and to several biased predictors derived from some popular biased ...

3 rd International Workshop on Linear Systems

The dth linear polarization constant of Rd

In [C. Benítez, Y. Sarantopoulos, A. Tonge, Lower bounds for norms of products of polynomials, Math. Proc. Cambridge Philos. Soc. 124 (3) (1998) 395–408] it was conjectured that for all unit vectors u1, . . . , ud in Rd , X (u1, . . . , ud ) := sup x∈Rd , |x|2=d d ∏ i=1 〈x,ui〉 1 with equality occurring iff u1, . . . , ud are orthonormal. We relate this to a conjecture about solutions of Ay = y−...

High-dimensional autocovariance matrices and optimal linear prediction

A new methodology for optimal linear prediction of a stationary time series is introduced. Given a sample X1, . . . , Xn, the optimal linear predictor of Xn+1 is X̃n+1 = φ1(n)Xn + φ2(n)Xn−1 + . . .+φn(n)X1. In practice, the coefficient vector φ(n) ≡ (φ1(n), φ2(n), . . . , φn(n)) is routinely truncated to its first p components in order to be consistently estimated. By contrast, we employ a consi...