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Uniformly minimum variance nonnegative quadratic unbiased estimation in a generalized growth curve model

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  • Wu, Xiaoyong
  • Zou, Guohua
  • Li, Yingfu

Abstract

Consider the generalized growth curve model subject to R(Xm)[subset, double equals]...[subset, double equals]R(X1), where Bi are the matrices of unknown regression coefficients, and and are independent and identically distributed with the same first four moments as a random vector normally distributed with mean zero and covariance matrix [Sigma]. We derive the necessary and sufficient conditions under which the uniformly minimum variance nonnegative quadratic unbiased estimator (UMVNNQUE) of the parametric function with C>=0 exists. The necessary and sufficient conditions for a nonnegative quadratic unbiased estimator with of to be the UMVNNQUE are obtained as well.

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Article provided by Elsevier in its journal Journal of Multivariate Analysis.

Volume (Year): 100 (2009)
Issue (Month): 5 (May)
Pages: 1061-1072

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Handle: RePEc:eee:jmvana:v:100:y:2009:i:5:p:1061-1072

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Keywords: 62H12 62J05 Generalized growth curve model UMVNNQUE;

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  1. Jemila Seid Hamid & Dietrich Von Rosen, 2006. "Residuals in the Extended Growth Curve Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(1), pages 121-138.
  2. Wu, Xiaoyong & Zou, Guohua & Chen, Jianwei, 2006. "Unbiased invariant minimum norm estimation in generalized growth curve model," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1718-1741, September.
  3. Mathew, T. & Niyogi, A. & Sinha, B. K., 1994. "Improved Nonnegative Estimation of Variance Components in Balanced Multivariate Mixed Models," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 83-101, October.
  4. M. S. Srivastava & Tatsuya Kubokawa, 1999. "Improved Nonnegative Estimation of Multivariate Components of Variance," CIRJE F-Series CIRJE-F-38, CIRJE, Faculty of Economics, University of Tokyo.
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