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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.

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.

Suggested Citation

  • Cohen, Guy & Francos, Joseph M., 2002. "Linear Least Squares Estimation of Regression Models for Two-Dimensional Random Fields," Journal of Multivariate Analysis, Elsevier, vol. 82(2), pages 431-444, August.
    • Handle: RePEc:eee:jmvana:v:82:y:2002:i:2:p:431-444
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    References listed on IDEAS

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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.
    2. David Rosenblatt, 1957. "On the graphs and asymptotic forms of finite boolean relation matrices and stochastic matrices," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 4(2), pages 151-167, June.
    3. DRYGAS, Hilmar, 1976. "Weak and strong consistency of the least squares estimators in regression models," LIDAM Reprints CORE 236, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    1. Rosa Espejo & Nikolai Leonenko & Andriy Olenko & María Ruiz-Medina, 2015. "On a class of minimum contrast estimators for Gegenbauer random fields," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 657-680, December.

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