×

Prediction for spatio-temporal models with autoregression in errors. (English) Zbl 1241.62132

Summary: In various environmental studies spatio-temporal correlated data are involved, so there has been an increasing demand for spatio-temporal prediction methods that capture spatio-temporal correlation so as to improve the accuracy of prediction. We propose a nonparametric iteration procedure for spatio-temporal models with specific autocorrelation structures. We extended the local linear method for spatial data to spatio-temporal local linear models, taking both spatial and temporal characteristics into consideration. The asymptotic normality of the predictors is established under mild conditions. The results of a simulation and case study also show that our predictors perform better than the traditional local linear method.

MSC:

62M30 Inference from spatial processes
62M40 Random fields; image analysis
62H12 Estimation in multivariate analysis
62G20 Asymptotic properties of nonparametric inference
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Anselin, L. The Moran Scatterplot as an ESDA tool to Assess Local Instability in Spatial Association. Paper Presented at the GISDATA Specialist Meeting on GIS and Spatial Analysis. December1–5, Amsterdam, The Netherlands. (Research Paper 9330, Regional Research Institute, West Virginia University)
[2] DOI: 10.1023/B:SISP.0000049116.23705.88 · Zbl 1125.62317 · doi:10.1023/B:SISP.0000049116.23705.88
[3] DOI: 10.1002/env.1005 · doi:10.1002/env.1005
[4] DOI: 10.2307/2286407 · Zbl 0423.62029 · doi:10.2307/2286407
[5] Cleveland W. S., Statistical Theory and Computational Aspects of Smoothing pp 10– (1996) · doi:10.1007/978-3-642-48425-4_2
[6] DOI: 10.2307/621469 · doi:10.2307/621469
[7] Cressie N. A.C., Statistics for Spatial Data (1993) · Zbl 1347.62005
[8] DOI: 10.1214/aos/1176344896 · Zbl 0427.62067 · doi:10.1214/aos/1176344896
[9] DOI: 10.1214/aos/1176342520 · Zbl 0281.60039 · doi:10.1214/aos/1176342520
[10] Deutsch S. J., Water Resources Bulletin 22 pp 967– (1986)
[11] DOI: 10.2307/1926785 · doi:10.2307/1926785
[12] DOI: 10.2307/2290637 · Zbl 0850.62354 · doi:10.2307/2290637
[13] DOI: 10.1214/aos/1176348900 · Zbl 0765.62040 · doi:10.1214/aos/1176348900
[14] Fan J., Journal of the Royal Statistical Society. Series B 57 pp 371– (1995)
[15] DOI: 10.1007/BF02511584 · doi:10.1007/BF02511584
[16] DOI: 10.1214/009053604000000850 · Zbl 1069.62075 · doi:10.1214/009053604000000850
[17] DOI: 10.1162/003465397556818 · doi:10.1162/003465397556818
[18] Ibragimov I. A., Independent and Stationary Sequences of Random Variables (1971) · Zbl 0219.60027
[19] DOI: 10.1016/j.csda.2004.02.011 · Zbl 1429.62426 · doi:10.1016/j.csda.2004.02.011
[20] DOI: 10.1111/j.1467-9892.2009.00612.x · Zbl 1223.62047 · doi:10.1111/j.1467-9892.2009.00612.x
[21] DOI: 10.1016/j.spl.2003.08.014 · Zbl 1058.62079 · doi:10.1016/j.spl.2003.08.014
[22] DOI: 10.1017/S0266466607070028 · doi:10.1017/S0266466607070028
[23] DOI: 10.1111/1467-9469.00056 · Zbl 0881.62047 · doi:10.1111/1467-9469.00056
[24] Moran P. A.P., Journal of the Royal Statistical Society B 10 pp 243– (1948)
[25] DOI: 10.1111/j.1540-6229.2009.00244.x · doi:10.1111/j.1540-6229.2009.00244.x
[26] DOI: 10.1002/env.710 · doi:10.1002/env.710
[27] DOI: 10.1016/S0167-7152(96)00140-X · Zbl 0901.62112 · doi:10.1016/S0167-7152(96)00140-X
[28] DOI: 10.1023/A:1007799028599 · doi:10.1023/A:1007799028599
[29] DOI: 10.1016/S0169-2070(99)00047-3 · doi:10.1016/S0169-2070(99)00047-3
[30] DOI: 10.1214/aos/1176325632 · Zbl 0821.62020 · doi:10.1214/aos/1176325632
[31] DOI: 10.1214/aos/1176343886 · Zbl 0366.62051 · doi:10.1214/aos/1176343886
[32] DOI: 10.1017/S026646660606004X · Zbl 1083.62037 · doi:10.1017/S026646660606004X
[33] DOI: 10.1007/s11146-005-1370-0 · doi:10.1007/s11146-005-1370-0
[34] Szummer M., Temporal Texture Modeling (1996) · doi:10.1109/ICIP.1996.560871
[35] DOI: 10.1080/10485250902783608 · Zbl 1165.62035 · doi:10.1080/10485250902783608
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.