An alternative look at the linear regression model

Oskar Maria Baksalary and Götz Trenkler
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Oskar Maria Baksalary: Adam Mickiewicz University
Götz Trenkler: Dortmund University of Technology

Statistical Papers, 2022, vol. 63, issue 5, No 5, 1499-1509

Abstract: Abstract An alternative look at the linear regression model is taken by proposing an original treatment of a full column rank model (design) matrix. In such a situation, the Moore–Penrose inverse of the matrix can be obtained by utilizing a particular formula which is applicable solely when a matrix to be inverted can be columnwise partitioned into two matrices of disjoint ranges. It turns out that this approach, besides simplifying derivations, provides a novel insight into some of the notions involved in the model and reduces computational costs needed to obtain sought estimators. The paper contains also a numerical example based on astronomical observations of the localization of Polaris, demonstrating usefulness of the proposed approach.

Keywords: Least squares method; Experimental data processing; Estimation theory; Moore–Penrose inverse; Columnwise partitioned matrix; Astronomical observations (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s00362-021-01280-x

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