Generalized inverses of partitioned matrices and recalculation of least squares estimates for data or model changes

Mitra, Sujit Kumar ; Bhimasankaram, P. (1971) Generalized inverses of partitioned matrices and recalculation of least squares estimates for data or model changes Sankhya - Series A, 33 (4). pp. 395-410. ISSN 0581-572X

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Official URL: http://sankhya.isical.ac.in/search/33a4/33a4037.ht...

Abstract

Let A be a m × n matrix and a be an m × 1 vector. In this paper, the authors have obtained formulae for computing several types of g-inverses of (A: α) from the corresponding g-inverses of A. Similar formulae are obtained for computing g-inverses of A from those of (A: α). These formulae are useful for revising least squares estimates in the following situations: (i) deletion or addition of an observation; and (ii) deletion or addition of a parameter in the linear model. Finally, the paper also gives formulae for computing g-inverses of A+BDC* from those of A when D is nonsingular.

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