ASYMPTOTIC DISTRIBUTIONS OF QUASI-MAXIMUM LIKELIHOOD ESTIMATORS FOR SPATIAL AUTOREGRESSIVE MODELS BY LUNG-FEI LEE

This paper investigates asymptotic properties of the maximim likelihood estimator and the quasi-maximum likelihood estimator for the spatial autoregressive model. The rates of convergence of those estimators may depend on some general features of the spatial weights matrix of the model. It is important to make the distinction with different spatial scenarios. Under the scenario that each unit will be influenced by only a few neighboring units, the estimators may have √ n-rate of convergence and be asymptotic normal. When each unit can be influenced by many neighbors, irregularity of the information matrix may occur and various components of the estimators may have different rates of convergence.

[1]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[2]  Lung-fei Lee,et al.  Best Spatial Two‐Stage Least Squares Estimators for a Spatial Autoregressive Model with Autoregressive Disturbances , 2003 .

[3]  Lung-fei Lee,et al.  CONSISTENCY AND EFFICIENCY OF LEAST SQUARES ESTIMATION FOR MIXED REGRESSIVE, SPATIAL AUTOREGRESSIVE MODELS , 2002, Econometric Theory.

[4]  Harry H. Kelejian,et al.  On the asymptotic distribution of the Moran I test statistic with applications , 2001 .

[5]  Giorgio Topa,et al.  Social interactions, local spillovers and unemployment , 2001 .

[6]  L. Anselin,et al.  Fast maximum likelihood estimation of very large spatial autoregression models: a characteristic polynomial approach , 2001 .

[7]  K. Bell,et al.  Applying the Generalized-Moments Estimation Approach to Spatial Problems Involving Micro-Level Data , 2000, Review of Economics and Statistics.

[8]  Timothy G. Conley.  GMM estimation with cross sectional dependence , 1999 .

[9]  Harry H. Kelejian,et al.  A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model , 1999 .

[10]  Jan K. Brueckner,et al.  Testing for Strategic Interaction Among Local Governments: The Case of Growth Controls , 1998 .

[11]  H. Kelejian,et al.  A Generalized Spatial Two-Stage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances , 1998 .

[12]  Murad S. Taqqu,et al.  Central limit theorems for quadratic forms with time-domain conditions , 1998 .

[13]  Luc Anselin,et al.  Spatial Dependence in Linear Regression Models with an Introduction to Spatial Econometrics , 1995 .

[14]  J. Davidson.  Stochastic Limit Theory , 1994 .

[15]  Halbert White,et al.  Estimation, inference, and specification analysis , 1996 .

[16]  Harvey S. Rosen,et al.  Budget spillovers and fiscal policy interdependence: Evidence from the states , 1993 .

[17]  Noel A Cressie,et al.  The asymptotic distribution of REML estimators , 1993 .

[18]  Robert Haining,et al.  Statistics for spatial data: by Noel Cressie, 1991, John Wiley & Sons, New York, 900 p., ISBN 0-471-84336-9, US $89.95 , 1993 .

[19]  C. Manski.  Identification of Endogenous Social Effects: The Reflection Problem , 1993 .

[20]  A. Case.  Spatial Patterns in Household Demand , 1991 .

[21]  B. Ripley.  Statistical inference for spatial processes , 1990 .

[22]  L. Anselin,et al.  Spatial Econometrics: Methods and Models , 1988 .

[23]  H. White.  Asymptotic theory for econometricians , 1985 .

[24]  K. Mardia,et al.  Maximum likelihood estimation of models for residual covariance in spatial regression , 1984 .

[25]  K. Ord.  Estimation Methods for Models of Spatial Interaction , 1975 .