ARTICLE
ABSTRACT
The spatial autoregressive (SAR) models are widely used in spatial econometrics for analyzing spatial data involving spatial autocorrelation structure. The present paper derives a Generalized Bayes estimator for estimating the parameters of a SAR model. The admissibility and minimaxity properties of the estimator have been discussed. For investigating the finite sample behaviour of the estimator, the results of a simulation study have been presented. The results of the paper are applied to demographic data on total fertility rate for selected Indian states.
KEYWORDS
spatial autoregressive model, prior and posterior distributions, generalized Bayes estimator, admissibility and minimaxity; total fertility rate (TFR)
REFERENCES
ANSELIN, L., (1988). Spatial econometrics, methods, and models, Dordrecht: Kluwer Academic.
ANSELIN, L., REY, S., (2010). Perspectives on spatial data analysis, Berlin: Springer, DOI:10.1007/978-3-642-01976-0.
BERGER, J., (1976). Admissible minimax estimation of a multivariate normal mean with arbitrary quadratic loss. Ann. Statist., 4, pp. 223–226.
BERGER, J. O., (1980): Statistical Decision Theory: Foundations, Concepts and Methods, Springer, N.Y.
BROWN, L. D., (1971). Admissible estimators, recurrent diffusions, and insoluble boundary value problems, Ann. Math. Statist., 42, pp. 855–903.
EFRON, B., MORRIS, C., (1976). Families of minimax estimators of the mean of a multivariate normal distribution. Ann. Statist., 4, pp. 11–21.
FOURDRINIER, D., STRAWDERMAN. W. E., WELLS, T., (1998). On the construction of Bayes minimax estimators, Ann. Statist., 26, pp. 660–671.
KUBOKAWA, T., (1991). An approach to improving the James-Stein estimator, J. Multivariate Anal., 36, pp. 121–126.
KUBOKAWA, T., (1994). An unified approach to improving equivariant estimators, Ann. Statist., 22, pp. 290–299.
LESAGE, J. P., (1998): Spatial Econometrics, www.spatial-econometrics.com.
LESAGE, J. P, PACE, R. K., (2009). Introduction to spatial econometrics, Boca Raton, FL: CRC, DOI:10.1201/9781420064254.
MARUYAMA, Y., (1998). A unified and broadened class of admissible minimax estimators of a multivariate normal mean, J. Multivariate Anal., 64, 196–205.
MARUYAMA, Y., (1999). Improving on the James-Stein Estimator, Statistics & Decisions, 17, pp. 137–140.
MARUYAMA, Y., (2000). Minimax admissible estimation of a multivariate normal mean and improvement upon the James-Stein estimator, Ph.D. dissertation, Graduate School of Economics, University of Tokyo.
PAL, A., CHATURVEDI, A., DUBEY, A., (2016). Shrinkage estimation in spatial autoregressive model, Journal of Multivariate Analysis, 143, pp. 362–373.
RUBIN, H. (1977). Robust Bayesian estimation, In Statistical Decision Theov and Related Topics II. (S. S. Gupta and D. S. Moore, eds.), Academic Press.
SCHABENBERGER, O., GOTWAY, C. A., (2005): Statistical Methods for Spatial Data Analysis, Chapman and Hall/CRC: Boca Raton, FL.
STEIN, C., (1973). Estimation of the mean of a multivariate normal distribution, In Proc. Prague Symp. Asymptotic Statist., pp. 345–381.
ZELLNER, A., (1986). On Assessing Prior Distributions and Bayesian Regression Analysis with g-Prior Distributions, In: Goel, P. and Zellner, A., Eds., Bayesian Inference and Decision Techniques: Essays in Honor of Bruno de Finetti, Elsevier Science Publishers, Inc., New York, pp. 233–243.
