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Linear Least Squares Estimation of Regression Models for Two-Dimensional Random Fields

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  • Cohen, Guy
  • Francos, Joseph M.
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    Abstract

    We consider the problem of estimating regression models of two-dimensional random fields. Asymptotic properties of the least squares estimator of the linear regression coefficients are studied for the case where the disturbance is a homogeneous random field with an absolutely continuous spectral distribution and a positive and piecewise continuous spectral density. We obtain necessary and sufficient conditions on the regression sequences such that a linear estimator of the regression coefficients is asymptotically unbiased and mean square consistent. For such regression sequences the asymptotic covariance matrix of the linear least squares estimator of the regression coefficients is derived.

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    File URL: http://www.sciencedirect.com/science/article/B6WK9-46C6GH2-9/2/fa51309242478e8ac85f6b8a0f72f577
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    Bibliographic Info

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

    Volume (Year): 82 (2002)
    Issue (Month): 2 (August)
    Pages: 431-444

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    Handle: RePEc:eee:jmvana:v:82:y:2002:i:2:p:431-444

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    Related research

    Keywords: two-dimensional random fields regression linear least squares estimation regression spectrum;

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    1. Lai, T. L. & Robbins, Herbert & Wei, C. Z., 1979. "Strong consistency of least squares estimates in multiple regression II," Journal of Multivariate Analysis, Elsevier, vol. 9(3), pages 343-361, September.
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