Generalized Additive Models for Gigadata: Modeling the U.K. Black Smoke Network Daily Data

Journal of the American Statistical Association

Volumn 112, Issue 519, 2017, Pages 1199-1210

  Wood, Simon N ^a   Li, Zheyuan ^b   Shaddick, Gavin ^b   Augustin, Nicole H ^b  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

^b University of Bath   (United Kingdom)

Author keywords

Air pollution; Big data; Parallel computing; Regression; Smoothing

Indexed keywords

EID: 85018208819     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.2016.1195744     Document Type: Article

References (58)

1. Augustin, N. H., Musio, M., von Wilpert, K., Kublin, E. Wood, S. N., and Schumacher, M., (2009), “Modeling Spatiotemporal Forest Health Monitoring Data,” Journal of the American Statistical Association, 104, 899–911.
2. Breslow, N. E., and Clayton, D. G., (1993), “Approximate Inference in Generalized Linear Mixed Models,” Journal of the American Statistical Association, 88, 9–25.
3. Ciocco, A., and Thompson, D., (1961), “A Follow-Up of Donora Ten Years After: Methodology and Findings,” American journal of Public Health Nations Health, 51, 155–164.
4. Claeskens, G., Krivobokova, T., and Opsomer, J. D., (2009), “Asymptotic Properties of Penalized Spline Estimators,” Biometrika, 96, 529–544.
5. Clifton, M., (1964), “Air Pollution,” Journal of the Royal Society of Medicine, 57, 615–618.
6. Craven, P., and Wahba, G., (1979), “Smoothing Noisy Data With Spline Functions,” Numerische Mathematik, 31, 377–403.
7. Currie, I. D., Durban, M., and Eilers, P. H., (2006), “Generalized Linear Array Models With Applications to Multidimensional Smoothing,” Journal of the Royal Statistical Society, Series B, 68, 259–280.
8. Diggle, P. J., Menezes, R., and Su, T.-l., (2010), “Geostatistical Inference Under Preferential Sampling,” Journal of the Royal Statistical Society, Series C, 59, 191–232.
9. Duchon, J., (1977), “Splines Minimizing Rotation-Invariant Semi-Norms in Solobev Spaces,” in Construction Theory of Functions of Several Variables, eds. W. Schemp and K. Zeller, Berlin: Springer, pp. 85–100.
10. Eilers, P. H., and Marx, B. D., (2003), “Multivariate Calibration With Temperature Interaction Using Two-Dimensional Penalized Signal Regression,” Chemometrics and Intelligent Laboratory Systems, 66(2), 159–174.
11. Eilers, P. H. C., and Marx, B. D., (1996), “Flexible Smoothing With B-Splines and Penalties,” Statistical Science, 11(2), 89–121.
12. Fahrmeir, L., and Lang, S., (2001), “Bayesian Inference for Generalized Additive Mixed Models Based on Markov Random Field Priors,” Applied Statistics, 50, 201–220.
13. Firket, J., (1936), “Fog Along the Meuse Valley,” Transactions of the Faraday Society, 32, 1191–1194.
14. Green, P. J., and Silverman, B. W., (1994), Nonparametric Regression and Generalized Linear Models, London: Chapman & Hall.
15. Gu, C., (1992), “Cross-Validating Non-Gaussian Data,” Journal of Computational and Graphical Statistics, 1, 169–179.
16. Gu, C., and Kim, Y. J., (2002), “Penalized Likelihood Regression: General Approximation and Efficient Approximation,” Canadian Journal of Statistics, 34(4), 619–628.
17. Hall, P., and Opsomer, J. D., (2005), “Theory For Penalised Spline Regression,” Biometrika, 92(1), 105–118.
18. Handcock, M. S., Meier, K., and Nychka, D., (1994), “Comment,” Journal of the American Statistical Association, 89(426), 401–403.
19. Hastie, T., and Tibshirani, R., (1986), “Generalized Additive Models” (with discussion), Statistical Science, 1, 297–318.
20. Hastie, T., and Tibshirani, R., (1990), Generalized Additive Models, London: Chapman & Hall.
21. Helwig, N. E., and Ma, P., (2016), “Smoothing Spline Anova for Super-Large Samples: Scalable Computation Via Rounding Parameters,” arXiv preprint arXiv:1602.05208.
22. Kammann, E. E., and Wand, M. P., (2003), “Geoadditive Models,” Applied Statistics, 52(1), 1–18.
23. Kauermann, G., Krivobokova, T., and Fahrmeir, L., (2009), “Some Asymptotic Results on Generalized Penalized Spline Smoothing,” Journal of the Royal Statistical Society, Series B, 71, 487–503.
24. Kimeldorf, G. S., and Wahba, G., (1970), “A Correspondence Between Bayesian Estimation on Stochastic Processes and Smoothing by Splines,” The Annals of Mathematical Statistics, 41, 495–502.
25. Lang, S., Umlauf, N., Wechselberger, P., Harttgen, K., and Kneib, T., (2014), “Multilevel Structured Additive Regression,” Statistics and Computing, 24, 223–238.
26. Li, Y., and Ruppert, D., (2008), “On the Asymptotics of Penalized Splines,” Biometrika, 95, 415–436.
27. Loader, A., (2002), Instruction manual: UK Smoke and Sulphur Dioxide Network, Culham Science Centre: Netcen, AEA Technology.
28. Lucas, C., (2004), “Lapack-Style Codes for Level 2 and 3 Pivoted Cholesky Factorizations,” LAPACK Working.
29. Marra, G., and Wood, S. N., (2012), “Coverage Properties of Confidence Intervals for Generalized Additive Model Components,” Scandinavian Journal of Statistics, 39, 53–74.
30. Marx, B. D., and Eilers, P. H., (1998), “Direct Generalized Additive Modeling With Penalized Likelihood,” Computational Statistics and Data Analysis, 28, 193–209.
31. McCullagh, P., and Nelder, J. A., (1989), Generalized Linear Models (2nd ed.), London: Chapman & Hall.
32. Miller, D. L., and Wood, S. N., (2014), “Finite Area Smoothing With Generalized Distance Splines,” Environmental and Ecological Statistics, 1–17.
33. Ministry of Health, (1954), Mortality and Morbidity During the London Fog of December 1952, London: HMSO.
34. Nocedal, J., and Wright, S., (2006), Numerical Optimization (2nd ed.), New York: Springer verlag.
35. Nychka, D., (1988), “Bayesian Confidence Intervals for Smoothing Splines,” Journal of the American Statistical Association, 83, 1134–1143.
36. of Terrain-50, C., (2015), OS Terrain 50: User Guide and Technical Specification, Adanac Drive, Southampton, SO16 0AS: Ordnance Survey.
37. OpenMP Architecture Review Board (2008, May). OpenMP application program interface version 3.0.
38. Parker, R., and Rice, J., (1985), Discussion of “Some Aspects of the Spline Smoothing Approach to Non-Parametric Regression Curve Fitting,” by Silverman, Journal of the Royal Statistical Society, Series B, 47, 40–42.
39. Perry, M., and Hollis, D., (2005a), “The Development of a New Set of Long-Term Climate Averages for the UK,” International Journal of Climatology, 25, 1023–1039.
40. Perry, M., and Hollis, D., (2005b), “The Generation of Monthly Gridded Datasets for a Range of Climatic Variables Over the UK,” International Journal of Climatology, 25, 1041–1054.
41. Quintana-Ortí, G., Sun, X., and Bischof, C. H., (1998), “A BLAS-3 Version of the QR Factorization With Column Pivoting,” SIAM Journal on Scientific Computing, 19, 1486–1494.
42. Reiss, P. T., and Ogden, T. R., (2009), “Smoothing Parameter Selection for a Class of Semiparametric Linear Models,” Journal of the Royal Statistical Society, Series B, 71, 505–523.
43. Rue, H., S. Martino, and Chopin, N., (2009), “Approximate Bayesian Inference for Latent Gaussian Models by Using Integrated Nested Laplace Approximations,” Journal of the Royal Statistical Society, Series B, 71(2), 319–392.
44. Ruppert, D., Wand, M. P., and Carroll, R. J., (2003), Semiparametric Regression, Cambridge, MA: Cambridge University Press.
45. Shaddick, G., and Zidek, J. V., (2014), “A Case Study in Preferential Sampling: Long Term Monitoring of Air Pollution in the UK,” Spatial Statistics, 9, 51–65.
46. Silverman, B. W., (1985), “Some Aspects of the Spline Smoothing Approach to Non-Parametric Regression Curve Fitting,” Journal of the Royal Statistical Society Series B, 47, 1–53.
47. Wahba, G., (1980), “Spline Bases, Regularization, and Generalized Cross Validation for Solving Approximation Problems With Large Quantities of Noisy Data,” in Approximation Theory III, eds. E. Cheney, London: Academic Press.
48. Wahba, G., (1981), “Spline Interpolation and Smoothing on the Sphere,” SIAM Journal on Scientific and Statistical Computing, 2, 5–16.
49. Wahba, G., (1983), “Bayesian Confidence Intervals for the Cross Validated Smoothing Spline,” Journal of the Royal Statistical Society, Series B, 45, 133–150.
50. Wahba, G., (1990), Spline Models for Observational Data, Philadelphia, PA: SIAM.
51. Wang, X., J., Shen, and Ruppert, D., (2011), “On the Asymptotics of Penalized Spline Smoothing,” Electronic Journal of Statistics, 5, 1–17.
52. Wood, S. N., (2003), “Thin Plate Regression Splines,” Journal of the Royal Statistical Society, Series B, 65, 95–114.
53. Wood, S. N., (2006), “Low-Rank Scale-Invariant Tensor Product Smooths for Generalized Additive Mixed Models,” Biometrics, 62, 1025–1036.
54. Wood, S. N., (2011), “Fast Stable Restricted Maximum Likelihood and Marginal Likelihood Estimation of Semiparametric Generalized Linear Models,” Journal of the Royal Statistical Society, Series B, 73(1), 3–36.
55. Wood, S. N., (2013), “On p-Values for Smooth Components of an Extended Generalized Additive Model,” Biometrika, 100, 221–228.
56. Wood, S. N., (2015), Core Statistics, Cambridge, MA: Cambridge University Press.
57. Wood, S. N., Goude, Y., and Shaw, S., (2015), “Generalized Additive Models for Large Data Sets,” Journal of the Royal Statistical Society, Series C, 64, 139–155.
58. Wood, S. N., Scheipl, F., and Faraway, J. J., (2013), “Straightforward Intermediate Rank Tensor Product Smoothing in Mixed Models,” Statistics and Computing, 23, 341–360.