On a Partitioned Inversion Formula Having Useful Applications 
In Econometrics

Faliva, Mario; Zoia, Maria Grazia

doi:10.1017/s0266466602182120

Cited by 14 publications

(7 citation statements)

References 4 publications

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“…The next result sheds some light on properties of M (V ) which is often referred to as a bordered matrix in the literature [8,10,18]. Proposition 3.3 (Finsler's lemma and bordered matrices).…”

Section: Optimization Of Quadratic Functionsmentioning

confidence: 80%

Matrix Support Functionals for Inverse Problems, Regularization, and Learning

Burke¹,

Hoheisel²

2015

SIAM J. Optim.

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A new class of matrix support functionals is presented which establish a connection between optimal value functions for quadratic optimization problems, the matrix-fractional function, the pseudo-matrix-fractional function, the nuclear norm, and multitask learning. The support function is based on the graph of the product of a matrix with its transpose. Closed form expressions for the support functional and its subdifferential are derived. In particular, the support functional is shown to be continuously differentiable on the interior of its domain, and a formula for the derivative is given when it exists.

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Section: Optimization Of Quadratic Functionsmentioning

confidence: 80%

Matrix Support Functionals for Inverse Problems, Regularization, and Learning

Burke¹,

Hoheisel²

2015

SIAM J. Optim.

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“…A recent result about partitioned inversion [1] together with newly found related results paves the way towards gaining new insights into linear estimation. Indeed, general closedform expressions for the best linear unbiased estimator (BLUE) and its dispersion matrix are obtained, which clear the ground for a thorough analysis of the BLU property for the ordinary least-squares (OLS) under nonsphericalness conditions.…”

Section: Introductionmentioning

confidence: 86%

New insights into best linear unbiased estimation and the optimality of least-squares

Faliva

Zoia

2006

Journal of Multivariate Analysis

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New results in matrix algebra applied to the fundamental bordered matrix of linear estimation theory pave the way towards obtaining additional and informative closed-form expressions for the best linear unbiased estimator (BLUE). The results prove significant in several respects. Indeed, more light is shed on the BLUE structure and on the working of the OLS estimator under nonsphericalness in (possibly) singular models.

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“…6 (2003) A recent result in partitioned inversion [2] paves the way to bridging this gap, as this paper will show, by finding an elegant solution to the estimation problem which, on the one hand, encompasses Theil's solution and, on the other, looks like a mirror image of the same.…”

Section: Journal Of Statistics and Management Systemsmentioning

confidence: 97%

“…For the proof of statement (i) and of the partitioned inversion formula (3.3) see Faliva and Zoia [2]. The partitioned inversion formula (3.4) is a standard result of the algebraic toolkit of econometricians (see e.g.…”

Section: A Useful Lemmamentioning

confidence: 99%