In this paper, we propose a Bayesian estimation method for the functional spatial error model. The Bayesian MCMC technique is used for the estimation of the parameters of the model. A simulation study is conducted for evaluating the performance of the proposed model. As an illustration, the proposed methodology is used to establish a relationship between unemployment and illiteracy in Senegal.

functional linear models, spatial dependence, Bayesian estimation, MCMC algorithms.

Received: August 21, 2023; Accepted: October 10, 2023; Published: December 30, 2023

How to cite this article: Alassane Aw, A Bayesian estimation method for the functional spatial error model, Far East Journal of Theoretical Statistics 68(1) (2024), 93-116. http://dx.doi.org/10.17654/0972086324006

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:
[1] M. Ahmed, Contribution to spatial statistics and functional data analysis, Ph. D. Thesis, 2017.
[2] L. Anselin, Spatial Econometrics: Methods and Models, Kluwer Academic Publishers, Dordrecht, 1988.
[3] A. Aw and E. N. Cabral, Functional SAC model: with application to spatial econometrics, South African Statist. J. 55(1) (2021), 1-13.
[4] A. Aw and E. N. Cabral, Bayesian estimation of the functional spatial lag model, Journal of Time Series Econometrics 12(2) (2020), 1-22.
[5] W. Caballero, R. Giraldo and J. Mateu, A universal kriging approach for spatial functional data, Stoch. Environ. Res. Risk Assess. 27 (2013), 1553-1563.
[6] G. Casella and E. I. Georg, Explaining the Gibbs sampler, Amer. Statist. 46(3) (1992), 167-174.
[7] T. T. Cai and P. Hall, Prediction in functional linear regression, Ann. Statist. 34 (2006), 2159-2179.
[8] H. Cardot, F. Ferraty and P. Sarda, Functional linear model, Statist. Probab. Lett. 45 (1999), 11-22.
[9] C. Comas, P. Delicado and J. Mateu, A second order approach to analyze spatial point patterns with functional marks, TEST 20 (2011), 503-523.
[10] C. Comas, L. Mehtatalo and J. Miina, Analysing space-time tree interdependencies based on individual tree growth functions, Stoch. Environ. Res. Risk Assess. 27 (2013), 1673-1681.
[11] S. Dabo-Niang and F. Yao, Kernel regression estimation for continuous spatial processes, Math. Methods Statist. 16 (2007), 298-317.
[12] W. R. Gilks, S. Richardson and D. Spiegelhalter, Markov Chain Monte Carlo in Practice, Chapman and Hall/CRC, 1995.
[13] R. Giraldo, P. Delicado and J. Mateu, Ordinary kriging for function-valued spatial data, Environ. Ecol. Stat. 18 (2011), 411-426.
[14] T. Hastie and C. Mallows, A statistical view of some chemometrics regression tools, Discussion. Technometrics 35 (1993), 140-143.
[15] L. Horváth and P. Kokoszka, Inference for Functional Data with Applications, Springer, 2012.
[16] T. Huang, G. Saporta, H. Wang and S. Wang, A robust spatial autoregressive scalar-on-function regression with t-distribution, Advances in Data Analysis and Classification 15 (2021), 57-81.
[17] H. H. Kelejian and I. R. Prucha, A generalized spatial two-stage least squares procedure for estimating a spatial autoregressive model with autoregressive disturbances, The Journal of Real Estate Finance and Economics 17(1) (1998), 99-121.
[18] G. Koop, D. J. Poirier and J. L. Tobias, Bayesian Econometric Methods, Cambridge University Press, New York, USA, 2007.
[19] J. P. Lesage, Bayesian estimation of spatial autoregressive models, International Regional Science Review 20(1-2) (1997), 113-129.
[20] J. P. LeSage and R. K. Pace, Introduction to Spatial Econometrics, 1st ed., CRC Press, 2009, 374 pp.
[21] W. Pineda-Rios, R. Giraldo and E. Porcu, Functional SAR models: with application to spatial econometrics, Spatial Statistics 29 (2019), 145-159.
[22] C. Preda and G. Saporta, PLS regression on a stochastic process, Comput. Statist. Data Anal. 48 (2005), 149-158.
[23] J. O. Ramsay and B. Silverman, Functional Data Analysis, Springer, 2005.
[24] G. O. Roberts and J. S. Rosenthal, General state space Markov chains and MCMC algorithms, Probab. Surv. 1 (2004), 20-71.
[25] L. Tierney, Markov chains for exploring posterior distributions, Ann. Statist. 22 (1994), 1701-1728.
[26] L. Zhang, V. Baladandayuthapani, H. Zhu, K. A. Baggerly, T. Majewski, B. A. Czerniak and J. S. Morris, Functional CAR models for large spatially correlated functional datasets, J. Amer. Statist. Assoc. 111 (2016), 772-786.