Fast smoothing parameter separation in multidimensional generalized P-splines: the SAP algorithm
Tóm tắt
Từ khóa
Tài liệu tham khảo
Breslow, N.E., Clayton, D.G.: Aproximated inference in generalised linear mixed models. J. Am. Stat. Assoc. 88, 9–25 (1993)
Currie, I., Durban, M., Eilers, P.H.C.: Generalized linear array models with applications to multidimensional smoothing. J. R. Stat. Soc. Ser. B 68, 259–280 (2006)
Currie, I., Durban, M.: Flexible smoothing with P-splines: a unified approach. Stat. Model. 4, 333–349 (2002)
de Boor, C.A.: A Practical Guide to Splines. Revised Edition. Springer, New York (2001)
Eilers, P.H.C., Marx, B.D.: Flexible smoothing with B-splines and penalties. Stat. Sci. 11, 89–121 (1996)
Eilers, P.H.C., Marx, B.D.: Multivariate calibration with temperature interaction using two-dimensional penalized signal regression. Chemom. Intell. Lab. Syst. 66, 159–174 (2003)
Eilers, P.H.C., Currie, I., Durban, M.: Fast and compact smoothing on large multidimensional grids. Comput. Stat. Data Anal. 50, 61–76 (2006)
Fahrmeir, L., Kneib, T., Lang, S.: Penalized structured additive regression for space-time data: a Bayesian perspective. Stat. Sin. 14, 715–745 (2004)
Gilmour, A.R., Thompson, R., Cullis, B.R.: Average information REML: an efficient algorithm for variance parameter estimation in linear mixed models. 51, 1440–1450 (1995)
Hastie, T.J., Tibshirani, R.J.: Generalized Additive Models. Chapman and Hall, London (1990)
Hastie, T.J., Tibshirani, R.J.: Varying-coefficient models. J. R. Stat. Soc. Ser. B 55, 757–796 (1993)
Harville, D.A.: Maximum likelihood approaches to variance component estimation and to related problems. J. Am. Stat. Assoc. 72, 320–338 (1977)
Johns, C., Nychka, D., Kittel, T., Daly, C.: Infilling sparse records of spatial fields. J. Am. Stat. Assoc. 98, 796–806 (2003)
Krivobokova, T., Crainiceanu, C.M., Kauermann, G.: Fast adaptive penalized splines. J. Comput. Graph. Stat. 17, 1–20 (2008)
Lee, D.-J.: Smothing mixed model for spatial and spatio-temporal data. PhD thesis, Department of Statistics, Universidad Carlos III de Madrid, Spain (2010)
Lee, D.-J., Durbán, M.: P-spline ANOVA-type interaction models for spatio-temporal smoothing. Stat. Model. 11, 49–69 (2011)
Lee, D.-J., Durbán, M., Eilers, P.H.C.: Efficient two-dimensional smoothing with P-spline ANOVA mixed models and nested bases. Comput. Stat. Data Anal. 61, 22–37 (2013)
Lin, X., Breslow, N.E.: Bias correction in generalized linear mixed models with multiple components of dispersion. J. Am. Stat. Assoc. 91, 1007–1016 (1996)
Lin, X., Zhang, D.: Inference in generalized additive mixed models using smoothing splines. J. R. Stat. Soc. Ser. B 61, 381–400 (1999)
Pawitan, Y.: In All Likelihood: Statistical Modelling and Inference Using Likelihood. Oxford University Press, USA (2001)
R Core Team. R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL http://www.R-project.org/ (2013)
Ruppert, D., Wand, M.P., Carroll, R.J.: Semiparametric Regression. Cambridge University Press, Cambridge (2003)
Schall, R.: Estimation in generalized linear models with random effects. Biometrika 78, 719–721 (1991)
Stiratelli, R., Laird, N.M., Ware, J.H.: Random effects models with serial observations with binary responses. Biometrics 40, 719–727 (1984)
Wood, S.N.: Stable and efficient multiple smoothing parameter estimation for generalized additive models. J. Am. Stat. Assoc. 99, 673–686 (2004)
Wood, S.N.: Generalized Additive Models. An introduction with R. Chapman & Hall/CRC, Boca Raton (2006a)
Wood, S.N.: Low-rank scale-invariant tensor product smooths for generalized additive models. J. R. Stat. Soc. Ser. B 70, 495–518 (2006b)
Wood, S.N.: Fast stable direct fitting and smoothness selection for generalized additive models. Biometrics 62, 1025–1036 (2008)
Wood, S.N.: Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models. J. R. Stat. Soc. Ser. B 73, 3–36 (2011)