409
Views
10
CrossRef citations to date
0
Altmetric
Original Articles

A Bayesian Approach to Parameter Estimation in the Presence of Spatial Missing Data

Pages 201-218 | Received 21 Jan 2015, Accepted 25 Aug 2015, Published online: 29 Oct 2015

References

  • Anderson, T. W. (1958) An Introduction to Multivariate Statistical Analysis, New York, NY, John Wiley.
  • Anselin, L. (1988) Spatial Econometrics: Methods and Models, Dordrecht, Kluwer Academic Publishers.
  • Benedetti, R. & Palma, D. (1994) Markov random field-based image subsampling method, Journal of Applied Statistics, 21(5), 495–509. doi: 10.1080/757584023
  • Bennett, R. J., Haining, R. P. & Griffith, D. A. (1984) The problem of missing data on spatial surfaces, Annals of the Association of American Geographers, 74(1), 138–156. doi: 10.1111/j.1467-8306.1984.tb01440.x
  • Besag, J. (1974) Spatial interaction and the statistical analysis of lattice systems, Journal of the Royal Statistical Society B, 36, 192–225.
  • Birkin, M. & Clarke, M. (1989) The generation of individual and household incomes at the small area level using synthesis, Regional Studies, 23, 535–548. doi: 10.1080/00343408912331345702
  • Brook, D. (1964) On the distinction between the conditional probability and the joint probability approaches in the specification of nearest-neighbour systems, Biometrika, 51, 481–483. doi: 10.1093/biomet/51.3-4.481
  • Carlin, B. P. & Banerjee, S. (2003) Hierarchical multivariate CAR models for spatio-temporally correlated survival data (with discussion), in: J. M. Bernardo, M. J. Bayarri, J. O. Berger, A. P. Dawid, D. Heckerman, A. F. M. Smith & M. West (eds) Bayesian Statistics vol. 7, pp. 45–63, Oxford, Oxford University Press.
  • Chun, Y. & Griffith, D. A. (2013) Spatial Statistics & Geostatistics, Thousand Oaks, CA, Sage.
  • Clayton, D. & Berardinelli, L. (1992) Bayesian methods for mapping disease risk, in: P. Elliott, J. Cuzick, D. English & R. Stern (eds) Geographical and Environmental Epidemiology: Methods for Small-Area Studies, pp. 205–220, Oxford, Oxford University Press.
  • Cliff, A. D. & Ord, J. K. (1973) Spatial Autocorrelation, London, Pion.
  • Cliff, A. D. & Ord, J. K. (1981) Spatial Processes, Models and Applications, London, Pion.
  • Conley, T. & Topa, G. (2002) Socio-economic distance and spatial patterns in unemployment, Journal of Applied Econometrics, 17(4), 303–327. doi: 10.1002/jae.670
  • Cressie, N. (1993) Statistics for Spatial Data, New York, NY, Wiley.
  • Dempster, A. P., Laird, N. M. & Rubin, D. P. (1977) Maximum likelihood estimation from incomplete data via the EM algorithm (with discussion), Journal of the Royal Statistical Society Series B, 39, 1–38.
  • Elhorst, J. P. (2010) Applied spatial econometrics: raising the bar, Spatial Economic Analysis, 5(1), 9–28. doi: 10.1080/17421770903541772
  • Fingleton, B. (2001) Equilibrium and economic growth: spatial econometric models and simulation, Journal of Regional Science, 41, 117–147. doi: 10.1111/0022-4146.00210
  • Fingleton, B. & McCombie, J. (1998) Increasing returns and economic growth: some evidence for manufacturing from the European Union regions, Oxford Economic Papers, 50, 89–105. doi: 10.1093/oxfordjournals.oep.a028638
  • Fischer, M. M. (2011) A spatial Mankiw-Romer-Weil model: theory and evidence, The Annals of Regional Science, 47, 419–436. doi: 10.1007/s00168-010-0384-6
  • Gaetan, C. & Guyon, X. (2010) Spatial Statistics and Modeling, New York, NY, Springer-Verlag.
  • Gelfand, A. E. & Vounatsou, P. (2003) Proper multivariate conditional autoregressive models for spatial data analysis, Biostatistics, 4(1), 11–15. doi: 10.1093/biostatistics/4.1.11
  • Griffith, D. A., Bennett, R. J. & Haining, R. P. (1989) Statistical analysis of spatial data in the presence of missing observations: a methodological guide and an application to urban census data, Environment & Planning A, 21, 1511–1523. doi: 10.1068/a211511
  • Griffith, D. & Layne, L. (1999) A Casebook for Spatial Statistical Data Analysis: A Compilation of Analyses of Different Thematic Data Sets, New York, NY, Oxford University Press.
  • Haining, R. P. (1978) The moving average model for spatial interaction, Transactions of the Institute of British Geographers New Series, 3(2), 202–225. doi: 10.2307/622202
  • Haining, R. P. (2003) Spatial Data Analysis: Theory and Practice, Cambridge, Cambridge University Press.
  • Haining, R. P., Griffith, D. A. & Bennett, R. J. (1984) A statistical approach to the problem of missing spatial data using a First-order Markov Model, Professional Geographer, 36(3), 338–345. doi: 10.1111/j.0033-0124.1984.00338.x
  • Haining, R. P., Griffith, D. A. & Bennett, R. J. (1989) Maximum likelihood estimation with missing spatial data and with an application to remotely sensed data, Communications in Statistics - Theory and Methods, 18, 1875–1894. doi: 10.1080/03610928908830008
  • Kelejian, H. H. & Prucha, I. R. (2010) Spatial models with spatially lagged dependent variable and incomplete data, Journal of Geographical System, 12, 241–257. doi: 10.1007/s10109-010-0109-5
  • Kennedy, S. & Tobler, W. R. (1983) Geographic interpolation, Geographical Analysis, 15, 151–156. doi: 10.1111/j.1538-4632.1983.tb00776.x
  • LeSage, J. P. & Fischer, M. M. (2008) Spatial growth regressions: model specification, estimation and interpretation, Spatial Economic Analysis, 3(3), 275–304. doi: 10.1080/17421770802353758
  • LeSage, J. P. & Pace, R. K. (2004) Models for spatially dependent missing data, Journal of Real Estate Finance and Economics, 29, 233–254. doi: 10.1023/B:REAL.0000035312.82241.e4
  • LeSage, J. P. & Pace, R. K. (2009) Introduction to Spatial Econometrics, Boca Raton, FL, Chapman & Hall/CRC Press.
  • Little, R. J. A. & Rubin, D. B. (1987) Statistical Analysis with Missing Data, New York, NY, John Wiley and Sons.
  • Longford, N. T. (2008) Studying Human Populations. An Advanced Course in Statistics, New York, NY, Springer.
  • Martin, R. J. (1984) Exact maximum likelihood for incomplete data from a correlated Gaussian process, Communications in Statistics - Theory and Method, 13, 1275–1288. doi: 10.1080/03610928408828754
  • Oakes, J. (1973) A forecasting approach to the missing data problem, Discussion paper presented at the Institute of British Geographers, Historical Geography Research Group, Birmingham.
  • Oh, M. S., Shin, D. W. & Kim, H. J. (2002) Bayesian analysis of regression models with spatially correlated errors and missing observations, Computational Statistics and Data Analysis, 39, 387–400. doi: 10.1016/S0167-9473(01)00084-6
  • Palma, D. & Benedetti, R. (1998) A transformational view of spatial data analysis, Geographical Systems, 5, 199–220.
  • Panzera, D. & Postiglione, P. (2014) Economic growth in Italian NUTS 3 provinces, The Annals of Regional Science, 53(1), 273–293. doi: 10.1007/s00168-014-0628-y
  • Pilz, J. (1991) Bayesian Estimation and Experimental Design in Linear Regression Models, New York, NY, John Wiley.
  • Piras, G., Postiglione, P. & Aroca, P. (2012) Specialization, R&D and productivity growth: evidence from EU regions, The Annals of Regional Science, 49(1), 35–51. doi: 10.1007/s00168-010-0424-2
  • Pons-Novell, J. & Viladecans-Marsal, E. (1999) Kaldor's laws and spatial dependence: evidence for the European regions, Regional Studies, 33(5), 443–451. doi: 10.1080/00343409950081284
  • Qiu, F. & Cromley, R. (2013) Special issue: areal interpolation and dasymetric modeling, Geographical Analysis, 45(3), 213–344.
  • Ripley, B. D. (1981) Spatial Statistics, New York, NY, John Wiley.
  • Rubin, D. B. (1987) Multiple Imputation for Nonresponse in Surveys, New York, NY, John Wiley and Sons.
  • Schafer, J. L. (1997) Analysis of Incomplete Multivariate Data, Boca Raton, FL, Chapman & Hall/CRC Press.
  • Strauss, D. J. (1977) Clustering on colored lattice, Journal of Applied Probability, 14, 135–143. doi: 10.2307/3213266
  • Tobler, W. R. (1979) Smooth pycnophylactic interpolation for geographical regions, Journal of the American Statistical Association, 74, 519–530. doi: 10.1080/01621459.1979.10481647
  • Tobler, W. R. & Kennedy, S. (1985) Smooth multi-dimensional interpolation, Geographical Analysis, 17, 251–257. doi: 10.1111/j.1538-4632.1985.tb00846.x
  • Wall, M. M. (2004) A close look at the spatial structure implied by the CAR and SAR models, Journal of Statistical Planning and Inference, 121, 311–324. doi: 10.1016/S0378-3758(03)00111-3
  • Whittle, P. (1954) On stationary process in the plane, Biometrika, 41, 434–449. doi: 10.1093/biomet/41.3-4.434
  • Willmott, C. & Wicks, D. E. (1980) An empirical method for the spatial interpolation of monthly precipitation within California, Physical Geography, 1, 59–73.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.