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More on partitioned possibly restricted linear regression

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  • Werner, Hans Joachim
  • Cemil Yapar
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    Abstract

    This paper deals with the general partitioned linear regression model where the regressor matrix $X=\pmatrix{X_1 & X_2\cr}$ may be deficient in column rank, the dispersion matrix $V$ is possibly singular, $\beta^t=\pmatrix{\beta_1^t & \beta_2^t\cr}$ - being partitioned according to $X$ - is the vector of unknown regression coefficients, and $\beta_2$ is possibly subject to consistent linear equality or inequality restrictions. In particular, we are interested in the set of {\it generalized least squares (GLS) selections} for $\beta_2$. Inspired by Aigner and Balestra [1], as well as by Nurhonen and Puntanen [2], we also consider a specific reduced model and describe a scenario under which the set of GLS selections for $\beta_2$ under the reduced model equals the set of GLS selections for $\beta_2$ under the original full model. The results obtained in [2] and [1] for the unrestricted {\it standard} (full rank) regression model are reobtained as special cases.

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    File URL: http://www.wiwi.uni-bonn.de/bgsepapers/bonsfb/bonsfb301.pdf
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    Bibliographic Info

    Paper provided by University of Bonn, Germany in its series Discussion Paper Serie B with number 301.

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    Length: pages
    Date of creation: 1994
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    Handle: RePEc:bon:bonsfb:301

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    Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
    Fax: +49 228 73 6884
    Web page: http://www.bgse.uni-bonn.de

    Related research

    Keywords: Gauss-Markov model; singular model; perfect multicollinearity; partitioned linear regression; linear equality constraints; linear inequality constraints; constrained generalized least squares selections; oblique projectors; generalized inverses.;

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    1. Aigner, Dennis J & Balestra, Pietro, 1988. "Optimal Experimental Design for Error Components Models," Econometrica, Econometric Society, vol. 56(4), pages 955-71, July.
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