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A note on the existence and uniqueness of quasi-maximum likelihood estimators for mixed regressive, spatial autoregression models

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  • Li, Mengyuan
  • Yu, Dalei
  • Bai, Peng
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    Abstract

    This note studies the existence and uniqueness of quasi-maximum likelihood estimator for mixed regressive, spatial autoregression model with continuously distributed response vector. Under very mild conditions that n>rank(Xn)+1 (n is the sample size and Xn is the n×p constant matrix of regressors), we show that the quasi-likelihood function has exactly one maximum with probability one in the parameter space.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 83 (2013)
    Issue (Month): 2 ()
    Pages: 568-572

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    Handle: RePEc:eee:stapro:v:83:y:2013:i:2:p:568-572

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    Related research

    Keywords: Existence; Mixed regressive; spatial autoregression model; Quasi-likelihood function; Quasi-maximum likelihood estimator; Uniqueness;

    References

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    1. Kelejian, Harry H & Prucha, Ingmar R, 1999. "A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(2), pages 509-33, May.
    2. Victor De Oliveira & Marco Ferreira, 2011. "Maximum likelihood and restricted maximum likelihood estimation for a class of Gaussian Markov random fields," Metrika, Springer, Springer, vol. 74(2), pages 167-183, September.
    3. Donald W.K. Andrews, 1999. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1229, Cowles Foundation for Research in Economics, Yale University.
    4. Lung-Fei Lee, 2004. "Asymptotic Distributions of Quasi-Maximum Likelihood Estimators for Spatial Autoregressive Models," Econometrica, Econometric Society, Econometric Society, vol. 72(6), pages 1899-1925, November.
    5. Lee, Lung-fei, 2007. "GMM and 2SLS estimation of mixed regressive, spatial autoregressive models," Journal of Econometrics, Elsevier, Elsevier, vol. 137(2), pages 489-514, April.
    6. Lee, Lung-Fei, 2002. "Consistency And Efficiency Of Least Squares Estimation For Mixed Regressive, Spatial Autoregressive Models," Econometric Theory, Cambridge University Press, vol. 18(02), pages 252-277, April.
    7. Smirnov, Oleg & Anselin, Luc, 2001. "Fast maximum likelihood estimation of very large spatial autoregressive models: a characteristic polynomial approach," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 35(3), pages 301-319, January.
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