Geoadditive models

Journal of the Royal Statistical Society. Series C: Applied Statistics

Volumn 52, Issue 1, 2003, Pages 1-18

  Kammann, E E ^a   Wand, M P ^a,b  

^a HARVARD UNIVERSITY   (United States)

^b HARVARD SCHOOL OF PUBLIC HEALTH   (United States)

Author keywords

Additive models; Disease mapping; Geostatistics; Kriging; Mixed models; Nonparametric regression; Penalized splines; Restricted maximum likelihood

Indexed keywords

EID: 0141575677     PISSN: 00359254     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9876.00385     Document Type: Article

References (61)

1. Booth, J. G. and Hobert, J. P. (1999) Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm. J. R. Statist. Soc. B, 61, 265-285.
2. Bowman, A. W. (1998) Discussion on 'Model-based geostatistics' (by P. J. Diggle, J. A. Tawn and R. A. Moyeed). Appl. Statist., 47, 334.
3. Bowman, A. W. and Azzalini, A. (1997) Applied Smoothing Techniques for Data Analysis. Oxford: Clarendon.
4. Breslow, N. E. and Clayton, D. G. (1993) Approximated inference in generalized linear mixed models. J. Am. Statist. Ass., 88, 9-25.
5. Brumback, B. A. and Rice, J. A. (1999) Smoothing spline models for the analysis of nested and crossed samples of curves (with discussion). J. Am. Statist. Ass., 93, 961-994.
6. Brumback, B. A., Ruppert, D. and Wand, M. P. (1999) Comment on Shively, Kohn and Wood. J. Am. Statist. Ass., 94, 794-797.
7. Chaudhuri, P. and Marron, J. S. (1999) SiZer for exploration of structures in curves. J. Am. Statist. Ass., 94, 807-823.
8. Crainiceanu, C., Ruppert, D. and Vogelsang, T. (2002) Probability that the MLE of a variance component is zero with applications to likelihood ratio tests. Cornell University, Ithaca. Unpublished.
9. Cressie, N. (1993) Statistics for Spatial Data. New York: Wiley.
10. Diggle, P. J., Tawn, J. A. and Moyeed, R. A. (1998) Model-based geostatistics (with discussion). Appl. Statist., 47, 299-350.
11. Durbán, M., Hackett, C., Currie, I. and Newton, A. (2000) Analysis of spatial trends in field trials using semi-parametric additive models. Unpublished.
12. Durbán Reguera, M. L. (1998) Modelling spatial trends and local competition effects using semiparametric additive models. PhD Thesis. Heriot-Watt University, Edinburgh.
13. Eilers, P. H. C. and Marx, B. D. (1996) Flexible smoothing with B-splines and penalties (with discussion). Statist. Sci., 11, 89-121.
14. French, J. L., Kammann, E. E. and Wand, M. P. (2001) Comment on paper by Ke and Wang. J. Am. Statist. Ass., 96, 1285-1288.
15. Gawande, A. (1999) The cancer-cluster myth. The New Yorker, Feb. 8th, 34-37.
16. Godtliebsen, F., Marron, J. S. and Chaudhuri, P. (2000) Significance in scale space. Unpublished.
17. Godtliebsen, F., Marron, J. S. and Chaudhuri, P. (2002) Significance in scale space for bivariate density estimation. J. Comput. Graph. Statist., 11, 1-22.
18. Gray, R. J. (1992) Spline-based tests in survival analysis. Biometrics, 50, 640-652.
19. Green, P. J. and Silverman, B. W. (1994) Nonparametric Regression and Generalized Linear Models. London: Chapman and Hall.
20. Handcock, M. S., Meier, K. and Nychka, D. (1994) Comment on paper by Laslett. J. Am. Statist. Ass., 89, 401-403.
21. Härdle, W., Hall, P. and Marron, J. S. (1988) How far are automatically chosen regression smoothing parameters from their optimum? J. Am. Statist. Ass., 83, 86-101.
22. Hastie, T. (1996) Pseudosplines. J. R. Statist. Soc. B, 58, 379-396.
23. Hastie, T. J. and Tibshirani, R. (1990) Generalized Additive Models. London: Chapman and Hall.
24. Heckman, N. E. (1986) Spline smoothing in a partly linear model. J. R. Statist. Soc. B, 48, 244-248.
25. Hobert, J. P., Altman, N. S. and Schofield, C. L. (1997) Analyses of fish species richness with spatial covariate. J. Am. Statist. Ass., 92, 846-854.
26. Johnson, M. E., Moore, L. M. and Ylvisaker, D. (1990) Minimax and maximin distance designs. J. Statist. Planng Inf., 26, 131-148.
27. Kammann, E. E. and Wand, M. P. (2001) Low-rank radial smoothing/kriging via restricted maximum likelihood. Harvard University, Boston. Unpublished.
28. Kelly, C. and Rice, J. (1990) Monotone smoothing with application to dose-response curves and the assessment of synergism. Biometrics, 46, 1071-1085.
29. Kelsall, J. E. and Diggle, P. J. (1998) Spatial variation in risk of disease: a nonparametric binary regression approach. Appl. Statist., 47, 559-573.
30. Lin, X. and Breslow, N. E. (1997) Bias correction in generalized linear mixed models with multiple components of dispersion. J. Am. Statist. Ass., 91, 1007-1016.
31. Lin, X. and Zhang, D. (1999) Inference in generalized additive mixed models by using smoothing splines. J. R. Statist. Soc. B, 61, 381-400.
32. Mardia, K. V. and Marshall, R. J. (1984) Maximum likelihood estimation of models for residual covariance in spatial regression. Biometrika, 72, 135-146.
33. Marx, B. D. and Eilers, P. H. C. (1998) Direct generalized additive modeling with penalized likelihood. Comput. Statist. Data Anal., 28, 193-209.
34. McCulloch, C. E. (1997) Maximum likelihood algorithms for generalized linear mixed models. J. Am. Statist. Ass., 92, 162-170.
35. Miller, J. J. (1977) Asymptotic properties of maximum likelihood estimates in the mixed model of the analysis of variance. Ann. Statist., 5, 746-762.
36. National Center for Health Statistics (1996) 1990 Birth cohort linked birth/infant death data set. CD-ROM Series 20, No. 6, SETS Version 1.22a. National Center for Health Statistics, Hyattsville.
37. Nychka, D. W. (2000) Spatial process estimates as smoothers. In Smoothing and Regression (ed. M. Schimek). Heidelberg: Springer.
38. Nychka, D. and Cummins, D. J. (1996) Comment on paper by Eilers and Marx. Statist. Sci., 11, 104-105.
39. Nychka, D., Haaland, P., O'Connell, M. and Ellner, S. (1998) FUNFITS, data analysis and statistical tools for estimating functions. Lect. Notes Statist.
40. Nychka, D. and Saltzman, N. (1998) Design of air quality monitoring networks. Lect. Notes Statist., 132, 51-76.
41. O'Connell, M. A. and Wolfinger, R. D. (1997) Spatial regression models, response surfaces, and process optimization. J. Comput. Graph. Statist., 6, 224-241.
42. O'Sullivan, F. (1986) A statistical perspective on ill-posed inverse problems (with discussion). Statist. Sci., 1, 505-527.
43. O'Sullivan, F. (1988) Fast computation of fully automated log-density and log-hazard estimators. SIAM J. Scient. Statist. Comput., 9, 363-379.
44. Parker, R. L. and Rice, J. A. (1985) Discussion on 'Some aspects of the spline smoothing approach to non-parametric curve fitting' (by B. W. Silverman). J. R. Statist. Soc. B, 47, 40-42.
45. Pinheiro, J. C. and Bates, D. M. (2000) Mixed-effects Models in S and S-PLUS. New York: Springer.
46. Ruppert, D. (2001) Empirical-bias bandwidths for local polynomial nonparametric regression and density estimation. J. Am. Statist. Ass., 92, 1049-1062.
47. Ruppert, D. and Carroll, R. J. (2000) Spatially-adaptive penalties for spline fitting. Aust. New Z. J. Statist., 42, 205-224.
48. Searle, S. R., Casella, G. and McCulloch, C. E. (1992) Variance Components. New York: Wiley.
49. Self, S. G. and Liang, K.-Y. (1997) Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions. J. Am. Statist. Ass., 82, 605-610.
50. Shively, T. S., Kohn, R. and Wood, S. (1999) Variable selection and function estimation in additive nonparametric regression using a data-based prior. J. Am. Statist. Ass., 94, 777-794.
51. Smith, M. and Kohn, R. (1996) Nonparametric regression using Bayesian variable selection. J. Econometr., 75, 317-344.
52. Speed, T. (1991) Comment on paper by Robinson. Statist. Sci., 6, 42-44.
53. Stein, M. L. (1999) Interpolation of Spatial Data: Some Theory for Kriging. New York: Springer.
54. Venables, W N. and Ripley, B. D. (1997) Modern Applied Statistics with S-PLUS. New York: Springer.
55. Verbyla, A. P., Cullis, B. R., Kenward, M. G. and Welham, S. J. (1999) The analysis of designed experiments and longitudinal data by using smoothing splines (with discussion). Appl. Statist., 48, 269-312.
56. Wahba, G. (1978) Improper priors, spline smoothing and the problem of guarding against model errors in regression. J. R. Statist. Soc. B, 40, 364-372.
57. Wahba, G. (1990) Spline Models for Observational Data. Philadelphia: Society for Industrial and Applied Mathematics.
58. Wang, Y. (1998) Mixed effects smoothing spline analysis of variance. J. R. Statist. Soc. B, 60, 159-174.
59. Wolfinger, R. and O'Connell, M. (1993) Generalized linear mixed models: a pseudo-likelihood approach. J. Statist. Computn Simuln, 48, 233-243.
60. Zeger, S. L. and Karim, M. R. (1993) Generalized linear models with random effects: a Gibbs sampling approach. J. Am. Statist. Ass., 86, 79-86.
61. Zimmerman, D. (1989) Computationally efficient restricted maximum likelihood estimation of generalized covariance functions. Math. Geol., 21, 655-672.