Mynbaev, Kairat and Ullah, Aman (2006): A Remark on the Asymptotic Distribution of the OLS Estimator for a Purely Autoregressive Spatial Model.

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Abstract
We derive the asymptotics of the OLS estimator for a purely autoregressive spatial model. Only lowlevel conditions are used. As the sample size increases, the spatial matrix is assumed to approach a squareintegrable function on the square $(0,1)^2$. The asymptotic distribution is a ratio of two infinite linear combinations of $\chi$square variables. The formula involves eigenvalues of an integral operator associated with the function approached by the spatial matrices. Under the conditions imposed identification conditions for the maximum likelihood method and methods of moments fail. A remedial iterative procedure using the OLS estimator is proposed.
Additional Information: This paper has been delivered at North American Summer Meeting of the Econometric Society in June 2006, see http://gemini.econ.umd.edu/conference/NASM2006/program/NASM2006.html. A revised and extended version (with computer simulations) has been accepted for publication as Mynbaev, K.T. and A. Ullah (2007) Asymptotic distribution of the OLS estimator for a purely autoregressive spatial model. Journal of Multivariate Analysis, doi: 10.1016/j.jmva.2007.04.002.
Item Type:  MPRA Paper 

Institution:  Economics Department, University of California at Riverside 
Original Title:  A Remark on the Asymptotic Distribution of the OLS Estimator for a Purely Autoregressive Spatial Model 
Language:  English 
Keywords:  spatial model; OLS estimator; asymptotic distribution; maximum likelihood; method of moments 
Subjects:  C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C21  CrossSectional Models ; Spatial Models ; Treatment Effect Models ; Quantile Regressions C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General 
Item ID:  3318 
Depositing User:  Kairat Mynbaev 
Date Deposited:  25. May 2007 
Last Modified:  12. Feb 2013 02:00 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/3318 