Premium
Least squares theory for possibly singular models
Author(s) -
Rao C. Radhakrishna
Publication year - 1978
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3314821
Subject(s) - invertible matrix , mathematics , moore–penrose pseudoinverse , least squares function approximation , covariance , generalized inverse , inverse , linear least squares , matrix (chemical analysis) , calculus (dental) , pure mathematics , linear model , statistics , geometry , chemistry , medicine , dentistry , estimator , chromatography
Abstract In a recent paper, Scobey (1975) observed that the usual least squares theory can be applied even when the covariance matrix σ 2 V of Y in the linear model Y = Xβ + e is singular by choosing the Moore‐Penrose inverse (V+XX′) + instead of V ‐1 when V is nonsingular. This result appears to be wrong. The appropriate treatment of the problem in the singular case is described.