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Estimating space and space-time covariance functions for large data sets: a weighted composite likelihood approach. (English) Zbl 1261.62088

Summary: We propose two methods for estimating space and space-time covariance functions from a Gaussian random field, based on the composite likelihood idea. The first method relies on the maximization of a weighted version of the composite likelihood function, while the second one is based on the solution of a weighted composite score equation. This last scheme is quite general and could be applied to any kind of composite likelihood. An information criterion for model selection based on the first estimation method is also introduced. The methods are useful for practitioners looking for a good balance between computational complexity and statistical efficiency. The effectiveness of the methods is illustrated through examples, simulation experiments, and by analyzing a data set on ozone measurements.

MSC:

62M40 Random fields; image analysis
62M09 Non-Markovian processes: estimation
62P12 Applications of statistics to environmental and related topics
65C60 Computational problems in statistics (MSC2010)
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References:

[1] Andersen E. W., Biostatistics 5 pp 15– (2004) · Zbl 1096.62108
[2] DOI: 10.1214/aos/1176350057 · Zbl 0602.62029
[3] Cressie N., Statistics for Spatial Data (revised ed.) (1993) · Zbl 1347.62005
[4] DOI: 10.2307/2669946 · Zbl 0999.62073
[5] Cressie N., Journal of the Royal Statistical Society, Series B 70 pp 209– (2008) · Zbl 05563351
[6] Curriero F., Journal of Agricultural, Biological and Environmental Statistics 4 pp 9– (1999)
[7] Doukhan P., Mixing. Properties and Examples (1994)
[8] Fuentes M., Journal of Geophysical Research 108 (24) pp 9002– (2003)
[9] Fuentes M., Journal of the American Statistical Association 102 pp 321– (2007) · Zbl 1284.62589
[10] Gilleland E., Environmetrics 16 pp 535– (2005)
[11] DOI: 10.1198/016214502760047113 · Zbl 1073.62593
[12] Guyon X., Random Fields on a Network (1995) · Zbl 0839.60003
[13] Heyde C., Quasi-Likelihood and Its Application: A General Approach to Optimal Parameter Estimation (1997) · Zbl 0879.62076
[14] DOI: 10.1890/04-0576
[15] DOI: 10.1198/016214507000000491 · Zbl 1469.86018
[16] Kaufman C. G., Journal of the American Statistical Association 103 pp 1545– (2008) · Zbl 1286.62072
[17] Kuk A., Biometrika 94 pp 939– (2007) · Zbl 1156.62012
[18] Lahiri S., Journal of Statistical Planning and Inference 103 pp 65– (2002) · Zbl 0989.62049
[19] Lee Y., Journal of the Royal Statistical Society, Series B 64 pp 837– (2002) · Zbl 1067.62100
[20] Li B., Bernoulli 14 pp 228– (2008) · Zbl 1155.62010
[21] Lindsay B., Contemporary Mathematics 80 pp 221– (1988)
[22] DOI: 10.1111/1467-9469.00058 · Zbl 1017.62088
[23] Sherman M., Journal of the Royal Statistical Society, Series B 58 pp 509– (1996)
[24] Stein M., Interpolation of Spatial Data. Some Theory of Kriging (1999) · Zbl 0924.62100
[25] Stein M., Journal of the Royal Statistical Society, Series B 67 pp 667– (2005) · Zbl 1101.62115
[26] Stein M., Journal of the Korean Statistical Society 37 pp 3– (2008) · Zbl 1196.62123
[27] Stein M., Journal of the Royal Statistical Society, Series B 66 pp 275– (2004) · Zbl 1062.62094
[28] Varin C., Biometrika 52 pp 519– (2005) · Zbl 1183.62037
[29] Vecchia A., Journal of the Royal Statistical Society, Series B 50 pp 297– (1988)
[30] Whittle P., Biometrika 49 pp 305– (1954)
[31] DOI: 10.1198/016214504000000241 · Zbl 1089.62538
[32] DOI: 10.1093/biomet/92.4.921 · Zbl 1151.62348
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