Radhakrishna Rao, C.
(1970)
*Estimation of heteroscedastic variances on a linear models*
Journal of the American Statistical Association, 65
(329).
pp. 161-172.
ISSN 0162-1459

Full text not available from this repository.

Official URL: http://www.jstor.org/stable/2283583

## Abstract

Let Y=Xβ + e be a Gauss-Markoff linear model such that E(e)=0 and D(e), the dispersion matrix of the error vector, is a diagonal matrix Δ whose ith diagonal element is σ_{i}^{2}, the variance of the ith observation y_{i}. Some of the s_{i}^{2} may be equal. The problem is to estimate all the different variances. In this article, a new method known as MINQUE (Minimum Norm Quadratic Unbiased Estimation) is introduced for the estimation of the heteroscedastic variances. This method satisfies some intuitive properties: (i) if S_{1} is the MINQUE of Σp_{i}σ_{i}^{2} and S_{2} that of Σq_{i}σ^{2}_{i}, then S_{1} + S_{2} is the MINQUE of Σ(p_{i} + q_{i})σ^{2}_{i}, (ii) it is invariant under orthogonal transformation, etc. Some sufficient conditions for the estimation of all linear functions of the σ^{2}_{i} are given. The use of estimated variances in problems of inference on the β parameters is briefly indicated.

Item Type: | Article |
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Source: | Copyright of this article belongs to American Statistical Association. |

ID Code: | 71486 |

Deposited On: | 28 Nov 2011 04:04 |

Last Modified: | 28 Nov 2011 04:04 |

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