Additive regression splines with total variation and non negative garrote penalties

References

• Antoniadis, A., I. Gijbels, and A. Verhasselt. 2012. Variable selection in additive models using p-splines. Technometrics 54 (4):425–38. doi:10.1080/00401706.2012.726000.
   Web of Science ®Google Scholar
• Breiman, L. 1995. Better subset regression using the nonnegative garrote. Technometrics 37 (4):373–84. doi:10.1080/00401706.1995.10484371.
   Web of Science ®Google Scholar
• Breiman, L., J. Friedman, C. Stone, and R. Olshen. 1984. Classification and regression trees. The Wadsworth and Brooks-Cole Statistics-Probability Series. Boca Raton, FL: Taylor & Francis.
   Google Scholar
• Breiman, L., and J. H. Friedman. 1985. Estimating optimal transformations for multiple regression and correlation. Journal of the American Statistical Association 80 (391):580–98. doi:10.1080/01621459.1985.10478157.
   Web of Science ®Google Scholar
• Cantoni, E., J. M. Flemming, and E. Ronchetti. 2011. Variable selection in additive models by non-negative garrote. Statistical Modelling 11 (3):237–52. doi:10.1177/1471082X1001100304.
   Web of Science ®Google Scholar
• Chouldechova, A., and T. Hastie. 2015. Generalized additive model selection. arXiv preprint arXiv:1506.03850.
   Google Scholar
• Cleveland, W. S., and C. Loader. 1996. Smoothing by local regression: Principles and methods. In Statistical theory and computational aspects of smoothing, 10–49. Heidelberg: Physica-Verlag HD.
   Google Scholar
• de Boor, C. 2001. A practical guide to splines. Applied mathematical sciences. New York: Springer.
   Google Scholar
• Eilers, P. H., and B. D. Marx. 1996. Flexible smoothing with b-splines and penalties. Statistical Science 11 (2):89–102. doi:10.1214/ss/1038425655.
   Web of Science ®Google Scholar
• Friedman, J., T. Hastie, H. Höfling, and R. Tibshirani. 2007. Pathwise coordinate optimization. The Annals of Applied Statistics 1 (2):302–32. doi:10.1214/07-AOAS131.
   Web of Science ®Google Scholar
• Harrison Jr, D., and D. L. Rubinfeld. 1978. Hedonic housing prices and the demand for clean air.
   Google Scholar
• Hastie, T., and R. Tibshirani. 1987. Generalized additive models: Some applications. Journal of the American Statistical Association 82 (398):371–86. doi:10.1080/01621459.1987.10478440.
   Web of Science ®Google Scholar
• Jhong, J.-H., J.-Y. Koo, and S.-W. Lee. 2017. Penalized b-spline estimator for regression functions using total variation penalty. Journal of Statistical Planning and Inference 184:77–93. doi:10.1016/j.jspi.2016.12.003.
   Web of Science ®Google Scholar
• Lin, Y., and H. H. Zhang. 2006. Component selection and smoothing in multivariate nonparametric regression. The Annals of Statistics 34 (5):2272–97. doi:10.1214/009053606000000722.
   Web of Science ®Google Scholar
• Meier, L., S. van de Geer, and P. Bühlmann. 2009. High-dimensional additive modeling. The Annals of Statistics 37 (6B):3779–821. doi:10.1214/09-AOS692.
   Web of Science ®Google Scholar
• Osborne, M. R., B. Presnell, and B. A. Turlach. 1998. Knot selection for regression splines via the lasso. Computing Science and Statistics 30:44–49.
   Google Scholar
• Ravikumar, P., J. Lafferty, H. Liu, and L. Wasserman. 2009. Sparse additive models. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 71 (5):1009–30. doi:10.1111/j.1467-9868.2009.00718.x.
   Web of Science ®Google Scholar
• Stone, C. J. 1985. Additive regression and other nonparametric models. The Annals of Statistics 13 (2):689–705. doi:10.1214/aos/1176349548.
   Web of Science ®Google Scholar
• Stone, C. J. 1986. The dimensionality reduction principle for generalized additive models. The Annals of Statistics 14 (2):590–606. doi:10.1214/aos/1176349940.
   Web of Science ®Google Scholar
• Storlie, C. B., H. D. Bondell, B. J. Reich, and H. H. Zhang. 2011. Surface estimation, variable selection, and the nonparametric oracle property. Statistica Sinica 21 (2):679. doi:10.5705/ss.2011.030a.
   PubMed Web of Science ®Google Scholar
• Tibshirani, R. 1996. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 58 (1):267–88.
   Web of Science ®Google Scholar
• Wahba, G. 1990. Spline models for observational data. Vol. 59. Philadelphia, PA: Siam.
   Google Scholar
• Wang, L., H. Li, and J. Z. Huang. 2008. Variable selection in nonparametric varying-coefficient models for analysis of repeated measurements. Journal of the American Statistical Association 103 (484):1556–69. doi:10.1198/016214508000000788.
   PubMed Web of Science ®Google Scholar
• Wood, S. N. 2000. Modelling and smoothing parameter estimation with multiple quadratic penalties. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 62 (2):413–28. doi:10.1111/1467-9868.00240.
   Web of Science ®Google Scholar
• Wood, S. N. 2001. mgcv: Gams and generalized ridge regression for R. R News 1 (2):20–25.
   Google Scholar
• Yuan, M., and Y. Lin. 2006. Model selection and estimation in regression with grouped variables. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 68 (1):49–67. doi:10.1111/j.1467-9868.2005.00532.x.
   Web of Science ®Google Scholar
• Yuan, M., and Y. Lin. 2007. On the non-negative garrotte estimator. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 69 (2):143–61. doi:10.1111/j.1467-9868.2007.00581.x.
   Web of Science ®Google Scholar
• Zhou, S., X. Shen, and D. Wolfe. 1998. Local asymptotics for regression splines and confidence regions. The Annals of Statistics 26 (5):1760–82. doi:10.1214/aos/1024691356.
   Web of Science ®Google Scholar