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Concentration Ellipsoids, Their Planes of Support, and the Linear Regression Model

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  • Alan J. Rogers

Abstract

The relationship between the concentration ellipsoid of a random vector and its planes of support is exploited to provide a geometric derivation and interpretation of existing results for a general form of the linear regression model. In particular, the planes of support whose points of tangency to the ellipsoid are contained in the range (or column space) of the design matrix are the source of all linear unbiased minimum variance estimators. The connection between this idea and estimators based on projections is explored, as is also its use in obtaining and interpreting some existing relative efficiency results.

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  • Alan J. Rogers, 2013. "Concentration Ellipsoids, Their Planes of Support, and the Linear Regression Model," Econometric Reviews, Taylor & Francis Journals, vol. 32(2), pages 220-243, February.
    • Handle: RePEc:taf:emetrv:v:32:y:2013:i:2:p:220-243
    DOI: 10.1080/07474938.2011.608055
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    1. Kapteyn, Arie & Fiebig, Denzil G., 1981. "When are two-stage and three-stage least squares estimators identical?," Economics Letters, Elsevier, vol. 8(1), pages 53-57.
    2. Schmidt, Peter, 1978. "A note on the estimation of seemingly unrelated regression systems," Journal of Econometrics, Elsevier, vol. 7(2), pages 259-261, June.
    3. Jorgen Grofi & Simo Puntanen, 2000. "Remark on pseudo-generalized least squares," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 139-144.
    4. Qian, Hailong & Schmidt, Peter, 2003. "Partial GLS regression," Economics Letters, Elsevier, vol. 79(3), pages 385-392, June.
    5. Phillips, P. C. B., 1979. "The concentration ellipsoid of a random vector," Journal of Econometrics, Elsevier, vol. 11(2-3), pages 363-365.
    6. Rao, C. Radhakrishna, 1973. "Representations of best linear unbiased estimators in the Gauss-Markoff model with a singular dispersion matrix," Journal of Multivariate Analysis, Elsevier, vol. 3(3), pages 276-292, September.
    7. Breusch, Trevor & Qian, Hailong & Schmidt, Peter & Wyhowski, Donald, 1999. "Redundancy of moment conditions," Journal of Econometrics, Elsevier, vol. 91(1), pages 89-111, July.
    8. Adrian Pagan, 1986. "Two Stage and Related Estimators and Their Applications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(4), pages 517-538.
    9. Gourieroux, Christian & Monfort, Alain, 1980. "Sufficient Linear Structures: Econometric Applications," Econometrica, Econometric Society, vol. 48(5), pages 1083-1097, July.
    10. repec:bla:ecorec:v:68:y:1992:i:200:p:65-72 is not listed on IDEAS
    11. Turkington, Darrell A, 1985. "A Note on Two-Stage Least Squares, Three-Stage Least Squares, and Maximum Likelihood Estimation in an Expectations Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(2), pages 507-510, June.
    12. BALESTRA, Pietro, 1970. "On the efficiency of ordinary least-squares in regression models," LIDAM Reprints CORE 71, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. Pagan, Adrian, 1984. "Econometric Issues in the Analysis of Regressions with Generated Regressors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(1), pages 221-247, February.
    14. Dwivedi, T. D. & Srivastava, V. K., 1978. "Optimality of least squares in the seemingly unrelated regression equation model," Journal of Econometrics, Elsevier, vol. 7(3), pages 391-395, April.
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