Estimation of heteroscedastic variances on a linear models

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

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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 σi2, the variance of the ith observation yi. Some of the si2 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 S1 is the MINQUE of Σpiσi2 and S2 that of Σqiσ2i, then S1 + S2 is the MINQUE of Σ(pi + qi2i, (ii) it is invariant under orthogonal transformation, etc. Some sufficient conditions for the estimation of all linear functions of the σ2i are given. The use of estimated variances in problems of inference on the β parameters is briefly indicated.

Item Type:Article
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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