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The estimation of a multivariate linear relation

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  • Robinson, P. M.

Abstract

A multivariate linear relation [eta]n = [beta]0[xi]n is considered, in which [xi]n and [eta]n are observed subject to white noise errors, with covariance matrices [sigma]0, [omega]0 respectively. If their elements lie in the null space of a suitable vector function, [beta]0, [sigma]0, [omega]0 may be uniquely defined by second-order functions of the data. The asymptotic properties of estimates of [beta]0, [sigma]0, [omega]0 are established under relatively mild conditions. We explore the possibility that explicit formulas for consistent estimates of [beta]0, [sigma]0, [omega]0 may be available.

Suggested Citation

  • Robinson, P. M., 1977. "The estimation of a multivariate linear relation," Journal of Multivariate Analysis, Elsevier, vol. 7(3), pages 409-423, September.
    • Handle: RePEc:eee:jmvana:v:7:y:1977:i:3:p:409-423
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    Cited by:

    1. Alexander Basilevsky, 1980. "The ratio estimator and maximum-likelihood weighted least squares regression," Quality & Quantity: International Journal of Methodology, Springer, vol. 14(3), pages 377-395, May.
    2. P. Bentler, 1986. "Structural modeling and psychometrika: An historical perspective on growth and achievements," Psychometrika, Springer;The Psychometric Society, vol. 51(1), pages 35-51, March.

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