Comparing and selecting spatial predictors using local criteria

Test

Volumn 24, Issue 1, 2015, Pages 1-28

  Bradley, Jonathan R ^a   Cressie, Noel ^b   Shi, Tao ^c  

^a UNIVERSITY OF MISSOURI   (United States)

^b UNIVERSITY OF WOLLONGONG   (Australia)

^c OHIO STATE UNIVERSITY   (United States)

Author keywords

Best linear unbiased predictor; Information criteria; Model averaging; Model combination

Indexed keywords

EID: 84925510994     PISSN: 11330686     EISSN: 18638260     Source Type: Journal    
DOI: 10.1007/s11749-014-0415-1     Document Type: Article

References (59)

1. Akaike H (1974) A new look at the statistical model identification. IEEE Trans Autom Control 19:716–723
2. Amari S, Murata N, Finke NMKR, Yang HH (1997) Asymptotic statistical theory of overtraining and cross-validation. IEEE Trans Neural Netw 8:985–996
3. Banerjee S, Carlin BP, Gelfand AE (2004) Hierarchical modeling and analysis for spatial data. Chapman and Hall, London
4. Banerjee S, Gelfand AE, Finley AO, Sang H (2008) Gaussian predictive process models for large spatial data sets. J Royal Stat Soc Ser B 70:825–848
5. Bradley JR, Cressie N, Shi T (2011) Selection of rank and basis functions in the spatial random effects model. In: Proceedings of the 2011 joint statistical meetings, American Statistical Association, Alexandria, pp 3393–3406
6. Bradley JR, Cressie N, Shi T (2012) Local spatial-predictor selection. In: Proceedings of the 2012 joint statistical meetings, American Statistical Association, Alexandria, pp 3098–3110
7. Burnham KP, Anderson DR (1998) Model selection and multimodel inference, 2nd edn. Springer, New York
8. Chahine M, Pagano T, Aumann H, Atlas R, Barnet C, Blaisdell J, Chen L, Divakarla M, Fetzer E, Goldberg M, Gautier C, Granger S, Hannon S, Irion FW, Kakar R, Kalnay E, Lambrigtsen B, Lee S, Marshall JL, McMillian WW, McMillin L, Olsen ET, Revercomb H, Rosenkranz P, Smith WL, Staelin D, Strow LL, Susskind J, Tobin D, Wolf W, Zhou L (2006) AIRS: improving weather forecasting and providing new data on greenhouse gases. Bull Am Meteorol Soc 87:911–926
9. Chen CS, Huang HC (2011a) Geostatistical model averaging based on conditional information criteria. Environ Ecol Stat 19:23–35
10. Chen C-S, Huang H-C (2011b) An improved Cp criterion for spline smoothing. J Stat Plan Inference 141:445–452
11. Chen Y-P, Huang H-C, Tu I-P (2010) A new approach for selecting the number of factors. Comput Stat Data Anal 54:2990–2998
12. Cressie N (1990) The origins of kriging. Math Geol 22:239–252
13. Cressie N (1993) Statistics for spatial data, rev edn. Wiley, New York
14. Cressie N, Johannesson G (2006) Spatial prediction for massive data sets. In: Proceedings of Australian academy of science Elizabeth and Frederick White conference. Australian Academy of Science, Canberra, pp 1–11
15. Cressie N, Johannesson G (2008) Fixed rank kriging for very large spatial data sets. J Royal Stat Soc Ser B 70:209–226
16. Cressie N, Shi T, Kang EL (2010) Using temporal variability to improve spatial mapping with application to satellite data. Can J Stat 38:271–289
17. Cressie N, Wikle CK (2011) Statistics for spatio-temporal data. Wiley, Hoboken
18. Donoho D, Johnstone I (1994) Ideal spatial adaptation by wavelet shrinkage. Biometrika 81:425–455
19. Efron B (1983) Estimating the error rate of a prediction rule: improvement on cross-validation. J Am Stat Assoc 78:316–331
20. Efron B (1986) How biased is the apparent error rate of a prediction rule? J Am Stat Assoc 81:461–470
21. Efron B (2004) The estimation of prediction error: covariance penalties and cross-validation. J Am Stat Assoc 99:619–642
22. Finley AO, Banerjee S, Carlin B (2012) Package ‘spBayes’. http://cran.r-project.org/web/packages/spBayes/spBayes.pdf, retrieved Jan 2013
23. Finley AO, Sang H, Banerjee S, Gelfand AE (2009) Improving the performance of predictive process modeling for large datasets. Comput Stat Data Anal 53:2873–2884
24. Greven S, Kneib T (2010) On the behaviour of marginal and conditional AIC in linear mixed models. Biometrika 97:773–789
25. Guyon I (1997) A scaling law for the validation-set training-set size ratio, technical report. Bell Laboratories, Berkeley
26. Hastie T, Tibshirani R, Friedman J (2009) The elements of statistical learning: data mining, inference, and prediction. Springer, New York
27. Huang HC, Chen CS (2007) Optimal geostatistical model selection. J Am Stat Assoc 102:1009–1024
28. Katzfuss M, Cressie N (2011a) Spatio-temporal smoothing and EM estimation for massive remote-sensing data sets. J Time Ser Anal 32:430–446
29. Katzfuss M, Cressie N (2011b) Tutorial on fixed rank kriging (FRK) of $${\rm CO}_2$$CO2 data. In: Proceedings of technical report, report no 858, Department of Statistics, The Ohio State University, Columbus. http://www.stat.osu.edu/sses/papers.html
30. Konishi S, Kitagawa G (1996) Generalised information criteria in model selection. Biometrika 83:875–890
31. Kullback S, Leibler RA (1951) On information and sufficiency. Ann Math Stat 22:79–86
32. Lai R, Huang H-C, Lee T (2012) Fixed and random effects selection in nonparametric additive mixed models. Electron J Stat 6:810–842
33. Landgrebe DA (2003) Signal theory methods in multispectral remote sensing. Wiley, Hoboken
34. Larsen J, Goutte C (1999) On optimal data split for generalization estimation and model selection. In: Proceedings IEEE workshop on neural networks for signal processing. IEEE Press, New York, pp 225–234
35. Liang H, Wu H, Zou G (2008) A note on conditional AIC for linear mixed-effects models. Biometrika 95:773–778
36. Lindgren F, Rue H, Lindström J (2011) An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach. J Royal Stat Soc Ser B 73:423–498
37. Mallows CL (1973) Some comments on Cp. Technometrics 15:661–675
38. Matheron G (1963) Principles of geostatistics. Econ Geol 58:1246–1266
39. Müller S, Scealy JL, Welsh AH (2013) Model selection in linear mixed models. Stat Sci 28:135–167
40. Nguyen H, Cressie N, Braverman A (2012) Spatial statistical data fusion for remote sensing applications. J Am Stat Assoc 107:1004–1018
41. Nychka D, Bandyopadhyay S, Hammerling D, Lindgren F, Sain S (2014) A multi-resolution Gaussian process model for the analysis of large spatial data sets. J Comput Gr Stat. doi:10.1080/10618600.2014.914946
42. Nychka DW (2014) Spatial process estimates as smoothers. In: Schmiek MG (ed) Smoothing and regression: approaches, computation and applications, rev edn. Wiley, New York, pp 393–424
43. Raftery A, Madigan D, Hoeting J (1997) Bayesian model averaging for linear regression models. J Am Stat Assoc 92:179–191
44. Ribeiro PJ Jr, Diggle PJ (2012) Package ‘geoR’. http://cran.r-project.org/web/packages/geoR/geoR.pdf, retrieved Nov 2012
45. Ripley BD (1996) Pattern recognition and neural networks. Press Syndicate of the University of Cambridge, New York
46. Ronchetti E (1997) Robustness aspects of model choice. Statistica Sinica 7:327–338
47. Ronchetti E, Staudte R (1994) A robust version of Mallow’s Cp. J Am Stat Assoc 89:550–559
48. Royle JA, Wikle CK (2005) Efficient statistical mapping of avian count data. Environ Ecol Stat 12:225–243
49. Rue H (2012) The R-INLA project. http://www.r-inla.org/, retrieved Nov 2012
50. Rue H, Martino S, Chopin N (2009) Approximate Bayesian inference for latent Gaussian models using integrated nested Laplace approximations. J Royal Stat Soc Ser B 71:319–392
51. Schabenberger O, Gotway C (2005) Statistical methods for spatial data analysis. CRC Press, Boca Raton
52. Schwarz GE (1978) Estimating the dimension of a model. Ann Stat 6:461–464
53. Shao J (1997) An asymptotic theory for linear model selection. Statistica Sinica 7:221–264
54. Shi T, Cressie N (2007) Global statistical analysis of MISR aerosol data: a massive data product from NASA’s Terra satellite. Environmetrics 18:665–680
55. Stein C (1981) Estimation of the mean of the multivariate normal distribution. Ann Stat 9:1135–1151
56. Vaida F, Blanchard S (2005) Conditional Akaike information for mixed-effects models. Biometrika 92:351–370
57. Wahba G (1990) Spline models for observational data. Society for Industrial and Applied Mathematics, Philadelphia
58. Wikle CK (2010) Low-rank representations for spatial processes. In: Gelfand AE, Diggle PJ, Fuentes M, Guttorp P (eds) Handbook of spatial statistics. CRC Press, Boca Raton, pp 107–118
59. Zhu J, Huang H-C, Reyes P (2010) On selection of spatial linear models for lattice data. J Royal Stat Soc Ser B 72:389–402