Abstract
The empirical likelihood ratio statistics are constructed for the parameters in spatial autoregressive models with spatial autoregressive disturbances. It is shown that the limiting distributions of the empirical likelihood ratio statistics are chi-squared distributions, which are used to construct confidence regions for the parameters in the models.
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References
Anselin, L. (1988). Spatial Econometrics: Methods and Models. Kluwer Academic Publishers, The Netherlands.
Anselin, L. and Bera, A.K. (1998). Spatial dependence in linear regression models with an introduction to spatial econometrics, Handbook of Applied Economics Statistics, ed. by Ullah A. and Giles, D. E A. Marcel Dekker, New York.
Chen, J. and Qin, J. (1993). Empirical likelihood estimation for finite populations and the effective usage of auxiliary information. Biometrika 80, 107–116.
Chen, S.X. and Keilegom, I.V. (2009). A review on empirical likelihood for regressions (with discussions). Test 3, 415–447.
Cliff, A.D. and Ord, J.K. (1973). Spatial Autocorrelation. Pion Ltd, London.
Cressien, N. (1993). Statistics for Spatial Data. Wiley, New York.
Jin, F. and Lee, L.F. (2019). GEL Estimation and tests of spatial autoregressive models. Journal of Econometrics, Forthcoming.
Kelejian, H.H. and Prucha, I.R. (2001). On the asymptotic distribution of the Moran I test statistic with applications. J. Econ. 104, 219–257.
Lee, L.F. (2004). Asymptotic distributions of quasi-maximum likelihood estimators for spatial autoregressive models. Econometrica 72, 1899–1925.
Liu, X., Lee, L.F. and Bollinger, C.R. (2010). An efficient GMM estimator of spatial autoregressive models. J. Econ. 159, 303–319.
Owen, A.B. (1988). Empirical likelihood ratio confidence intervals for a single functional. Biometrika 75, 237–249.
Owen, A.B. (1990). Empirical likelihood ratio confidence regions. Ann. Statist. 18, 90–120.
Owen, A.B. (2001). Empirical Likelihood. Chapman & Hall, London.
Qin, J. and Lawless, J. (1994). Empirical likelihood and general estimating equations. Ann. Statist. 22, 300–325.
Wu, C.B. (2004). Weighted empirical likelihood inference. Statist. Probab. Lett. 66, 67–79.
Zhong, B. and Rao, J.N.K. (2000). Empirical likelihood inference under stratified random sampling using auxiliary population information. Biometrika 87, 929–938.
Acknowledgements
This work was partially supported by the National Natural Science Foundation of China (11671102), the Natural Science Foundation of Guangxi (2016GXNSFAA3800163, 2017GXNSFAA198349) and the Program on the High Level Innovation Team and Outstanding Scholars in Universities of Guangxi Province.
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Qin, Y. Empirical Likelihood for Spatial Autoregressive Models with Spatial Autoregressive Disturbances. Sankhya A 83, 1–25 (2021). https://doi.org/10.1007/s13171-019-00166-3
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DOI: https://doi.org/10.1007/s13171-019-00166-3