Fast smoothing parameter separation in multidimensional generalized P-splines: the SAP algorithm

Statistics and Computing - Tập 25 Số 5 - Trang 941-957 - 2015
María Xosé Rodríguez‐Álvarez1, Dae‐Jin Lee2, Thomas Kneib3, Maŕıa Durbán4, Paul H.C. Eilers5
1Department of Statistics and Operations Research, University of Vigo, Campus Lagoas-Marcosende s/n, 36310 , Vigo, Spain
2CSIRO Computational Informatics, Clayton, VIC, Australia
3Chair of Statistics, Georg-August-Universität Göttingen, Göttingen, Germany
4Department of Statistics, Universidad Carlos III de Madrid, Leganés, Spain
5Erasmus Medical Center, Rotterdam, the Netherlands

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)

Lang, S., Brezger, A.: Bayesian P-splines. J. Comput. Grap. Stat. 13, 183–212 (2004)

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)

Wand, M.P.: Smoothing and mixed models. Comput. Stat. 18, 223–249 (2003)

Wood, S.N.: Thin plate regression splines. J. R. Stat. Soc. Ser. B 65, 95–114 (2003)

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)

Wood, S.N., Scheipl, F., Faraway, J.J.: Straightforward intermediate rank tensor product smoothing in mixed models. Stat. Comput. 23, 341–360 (2013)