342
Views
12
CrossRef citations to date
0
Altmetric
Original Articles

Asymptotics for penalised splines in generalised additive models

&
Pages 269-289 | Received 12 Jun 2013, Accepted 17 Feb 2014, Published online: 21 Mar 2014

References

  • Aerts, M., Claeskens, G., and Wand, M.P. (2002), ‘Some Theory for Penalized Spline Generalized Additive Models’, Journal of Statistical Planning and Inference, 103, 455–470. doi: 10.1016/S0378-3758(01)00237-3
  • Agarwal, G., and Studden, W. (1980), ‘Asymptotic Integrated Mean Square Error Using Least Squares and Bias Minimizing Splines’, The Annals Statistics, 8, 1307–1325. doi: 10.1214/aos/1176345203
  • Antoniadis, A., Gijbels, I., and Verhasselt, A. (2012), ‘Variable Selection in Additive Models Using P-Splines’, Technometrics, 54, 425–438. doi: 10.1080/00401706.2012.726000
  • Barrow, D.L., and Smith, P.W. (1978), ‘Asymptotic Properties of Best L2[0, 1] Approximation by Splines with Variable Knots’, The Quarterly of Applied Mathematics, 36, 293–304.
  • de Boor, C. (2001), A Practical Guide to Splines, New York: Springer-Verlag.
  • Breslow, N.E., and Clayton, D.G. (1993), ‘Approximate Inference in Generalized Linear Mixed Models’, Journal of the American Statistical Association, 88, 9–25.
  • Claeskens, G., Krivobokova, T., and Opsomer, J.D. (2009), ‘Asymptotic Properties of Penalized Spline Estimators’, Biometrika, 96, 529–544. doi: 10.1093/biomet/asp035
  • Cook, D., and Dabrera, R.C. (1998), ‘Partial Residual Plots in Generalized Linear Models’, Journal of the American Statistical Association, 93, 730–739. doi: 10.1080/01621459.1998.10473725
  • Eilers, P.H.C., and Marx, B.D. (1996), ‘Flexible Smoothing with B-Splines and Penalties’, Statistical Science, 11, 89–121 (with Discussion). doi: 10.1214/ss/1038425655
  • Fan, J., Feng, Y., and Song, R. (2011), ‘Nonparametric Independence Screening in Sparse Ultra-High-Dimensional Additive Models’, Journal of the American Statistical Association, 106, 544–557. doi: 10.1198/jasa.2011.tm09779
  • Hall, P., and Opsomer, J.D. (2005), ‘Theory for Penalized Spline Regression’, Biometrika, 92, 105–118. doi: 10.1093/biomet/92.1.105
  • Hastie, T., and Tibshirani, R. (1990), Generalized Additive Models, London: Chapman and Hall.
  • Horn, R.A., and Johnson, C.A. (1985), Matrix Analysis, Cambridge: Cambridge University Press.
  • Horowitz, J., and Mammen, E. (2004), ‘Nonparametric Estimation of an Additive Model with a Link Function’, The Annals of Statistics, 32, 2412–2443. doi: 10.1214/009053604000000814
  • Horowitz, J., Klemelaä, J., and Mammen, E. (2006), ‘Optimal Estimation in Additive Regression Models’, Bernoulli, 12, 271–298. doi: 10.3150/bj/1145993975
  • Huang, J., Horowitz, J.J., and Wei, F. (2010), ‘Variable Selection in Nonparametric Additive Models’, The Annals of Statistics, 38, 2282–2313. doi: 10.1214/09-AOS781
  • 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. doi: 10.1111/j.1467-9868.2008.00691.x
  • Landwehr, J.M., Pregibon, D., and Shoemaker, A.C. (1984), ‘Graphical Methods for Assessing Logistic Regression Models’, Journal of the American Statistical Association, 79, 61–71. doi: 10.1080/01621459.1984.10477062
  • Lin, X., and Zhang, D. (1999), ‘Inference in Generalized Additive Mixed Models by Using Smoothing Splines’, Journal of Royal Statistical Society, Series B, 61, 381–400. doi: 10.1111/1467-9868.00183
  • Linton, O.B. (2000), ‘Inference in Generalized Additive Mixed Models by Using Smoothing Splines’, Journal of Royal Statistical Society, Series B, 61, 381–400. doi: 10.1111/1467-9868.00183
  • Marx, B.D., and Eilers, P.H.C. (1998), ‘Direct Generalized Additive Modeling with Penalized Likelihood’, Computational Statistics & Data Analysis, 28, 193–209. doi: 10.1016/S0167-9473(98)00033-4
  • McCullagh, J., and Nelder, J.A. (1989), Generalized Linear Models (2nd ed.), London: Chapman and Hall.
  • Meier, L., Geer, S.V., and Bühlman, P. (2009), ‘High-Dimensional Additive Modeling’, The Annals of Statistics, 37, 3779–3821. doi: 10.1214/09-AOS692
  • Opsomer, J.D. (2000), ‘Asymptotic Properties of Backfitting Estimators’, Journal of Multivariate Analysis, 73, 166–179. doi: 10.1006/jmva.1999.1868
  • O'Sullivan, F. (1986), ‘A Statistical Perspective on Ill-Posed Inverse Problems’, Statistical Science, 1, 505–527 (with discussion).
  • Ruppert, D., Wand, M.P., and Carroll, R.J. (2003), Semiparametric Regression, Cambridge: Cambridge University Press.
  • Sheather, S.J., and Jones, M.C. (1991), ‘A Reliable Data-Based Bandwidth Selection Method for Kernel Density Estimation’, Journal of Royal Statistical Society, 53, 683–690.
  • Wand, M.P. (1999), ‘A Central Limit Theorem for Local Polynomial Backfitting Estimators’, Journal of Multivariate Analysis, 70, 57–65. doi: 10.1006/jmva.1999.1812
  • Wang, X., Shen, J., and Ruppert, D. (2011), ‘On the Asymptotics of Penalized Spline Smoothing’, Electronic Journal of Statistics, 5, 1–17. doi: 10.1214/10-EJS593
  • Wood, S.N. (2006), Generalized Additive Models: An Introduction with R, CRC: Chapman and Hall.
  • Yoshida, T., and Naito, K. (2012), ‘Asymptotics for Penalized Additive B-Spline Regression’, Journal of Japan Statistical Society, 42, 81–107. doi: 10.14490/jjss.42.81
  • Yu, K., Park, B.U., and Mammen, E. (2008), ‘Smooth Backfitting in Generalized Additive Models’, The Annals of Statistics, 36, 228–260. doi: 10.1214/009053607000000596

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.