We study the degrees of freedom in shrinkage estimation of the regression coefficients. Generalizing the idea of the Lasso, we consider the problem of estimating the coefficients by the projection of the ordinary least squares estimator onto a closed convex set. Then an unbiased estimator of the degrees of freedom is derived in terms of geometric quantities under a smoothness condition on the b...

− The spectrophotometric analysis of oil mixtures, containing olive oil, is the subject of this paper. Its objective is to propose and evaluate a new methodology for determination of a selected component of such a mixture. According to this methodology, the space of concentration values to be estimated is partitioned into subspaces and the calibration is performed separately for each subspace b...

B-splines can be used to approximate data in a variety of metrology applications. In general, the approximation is carried out so as to minimize a criterion deened in terms of the least squares norm. However, often this choice of norm is inappropriate , and a measure such as thè 1 or minimax norm should be chosen. In this tutorial paper, we introduce the topic of B-splines, and we discuss the a...

This paper establishes that when using a least squares criterion to estimate an output error type model structure, then the measurement noise induced variability of the frequency response estimate depends on the estimated (and hence also on the true) pole positions. This dependence on pole position is perhaps counter to prevailing wisdom that for any ‘shift invariant’ model structure, the varia...

Reportedly, standard identiication algorithms do not guarantee the controllability of the estimated system. In this paper, a penalized least squares (PLS) identiication criterion is proposed to overcome this diiculty. The criterion is shown to provide estimated systems which exhibit an uniform controllability property through time. Moreover, the Lai and Wei upper bound for the least squares est...

Recently it has been shown (Afonine et al, 2001; Lunin et al., 2002) that the approximation of the maximum likelihood criterion (ML) by a quadratic functional (Lunin & Urzhumtsev, 1999) allows to understand the features of the ML refinement and its advantages with respect to the traditional least-squares (LS) refinement. In this latter, the magnitudes { } S calc F ∈ s s of structure factors cal...

An adaptive control problem for some continuous-time linear stochastic systems and its solution are presented in this paper. The solution includes showing the strong consistency of a family of maximum likelihood (or, equivalently, least squares) estimates of the unknown parameters and the convergence of the average quadratic costs with control based on these estimates to the optimal cost. The s...

Abstract: This paper establishes that when using a least squares criterion to estimate an output error type model structure, then the measurement noise induced variability of the frequency response estimate depends on the estimated (and hence also on the true) pole positions. This dependence on pole position is perhaps counter to prevailing wisdom that for any ‘shift invariant’ model structure,...