Radhakrishna Rao, C.
(1974)
*Projectors, generalized inverses and the BLUE's*
Journal of the Royal Statistical Society - Series B: Statistical Methodology, 36
(3).
pp. 442-448.
ISSN 1369-7412

Full text not available from this repository.

Official URL: http://www.jstor.org/stable/2984930

## Abstract

It is well known that in the Gauss-Markov model (Y, Xβ, σ^{2}V) with |V| ≠ 0, the BLUE (best linear unbiased estimator) of Xβ is Y_{1}, the orthogonal projection of Y on M(X), the space spanned by the columns of X, with inner product defined as (x, y)=x'V^{−1}y. A quadratic function of Y_{2}, the projection of Y on the orthogonal complement of M(X), provides an estimate of σ^{2}. It may be seen that Y=Y_{1}+Y_{2}. When V is singular, the inner product definition as in non-singular case is not possible. In this paper a suitable theory of projection operators is developed for the case |V|=0, and a decomposition Y=Y_{1}+Y_{2} is obtained such that Y_{1} is the BLUE of Xβ and a quadratic function of Y_{2} is the MINQUE (Minimum Norm Quadratic Unbiased Estimator) of σ^{2} in the sense of Rao (1972).

Item Type: | Article |
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Source: | Copyright of this article belongs to John Wiley and Sons. |

Keywords: | Gauss-Markov Model; Blue; Minque; Projection Operator; G-inverse; Singular Dispersion Matrix |

ID Code: | 54754 |

Deposited On: | 12 Aug 2011 13:19 |

Last Modified: | 12 Aug 2011 13:19 |

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