Shape constrained additive models
Tóm tắt
Từ khóa
Tài liệu tham khảo
Akaike, H.: Information theory and an extension of the maximum likelihood principle. In: Petrov, B.N., Csaki, B.F. (eds.) Second International Symposium on Information Theory. Academiai Kiado, Budapest (1973)
Bollaerts, K., Eilers, P., van Mechelen, I.: Simple and multiple P-splines regression with shape constraints. Br. J. Math. Stat. Psychol. 59, 451–469 (2006)
Brezger, A., Steiner, W.: Monotonic regression based on Bayesian P-splines: an application to estimating price response functions from store-level scanner data. J. Bus. Econ. Stat. 26(1), 90–104 (2008)
Claeskens, G., Krivobokova, T., Opsomer, J.: Asymptotic properties of penalized spline estimators. Biometrica 96(3), 529–544 (2009)
Dunson, D.: Bayesian semiparametric isotonic regression for count data. J. Am. Stat. Assoc. 100(470), 618–627 (2005)
Dunson, D., Neelon, B.: Bayesian inference on order-constrained parameters in generalized linear models. Biometrics 59, 286–295 (2003)
Elliott, P., Shaddick, G., Kleinschmidt, I., Jolley, D., Walls, P., Beresford, J., Grundy, C.: Cancer incidence near municipal solid waste incinerators in Great Britain. Br. J. Cancer 73, 702–710 (1996)
Fritsch, F., Carlson, R.: Monotone piecewise cubic interpolation. SIAM J. Numer. Anal. 17(2), 238–246 (1980)
Golub, G., van Loan, C.: Matrix Computations, 3rd edn. Johns Hopkins University Press, Baltimore (1996)
Hastie, T., Tibshirani, R.: Generalized Additive Models. Chapman & Hall, New York (1990)
He, X., Shi, P.: Monotone B-spline smoothing. J. Am. Stat. Assoc. 93(442), 643–650 (1998)
Holmes, C., Heard, N.: Generalized monotonic regression using random change points. Stat. Med. 22, 623–638 (2003)
Kauermann, G., Krivobokova, T., Fahrmeir, L.: Some asymptotic results on generalized penalized spline smoothing. J. R. Stat. Soc. B 71(2), 487–503 (2009)
Kauermann, G., Opsomer, J.: Data-driven selection of the spline dimension in penalized spline regression. Biometrika 98(1), 225–230 (2011)
Kelly, C., Rice, J.: Monotone smoothing with application to dose-response curves and the assessment of synergism. Biometrics 46, 1071–1085 (1990)
Kim, Y.-J., Gu, C.: Smoothing spline gaussian regression: more scalable computation via efficient approximation. J. R. Stat. Soc: Ser. B. 66(2), 37–356 (2004)
Marra, G., Wood, S.N.: Coverage properties of confidence intervals for generalized additive model components. Scand. J. Stat. 39(1), 53–74 (2012)
Meyer, M.: Inference using shape-restricted regression splines. Ann. Appl. Stat. 2(3), 1013–1033 (2008)
Meyer, M., Woodroofe, M.: On the degrees of freedom in shape-restricted regression. Ann. Stat. 28(4), 1083–1104 (2000)
Nychka, D.: Bayesian confidence intervals for smoothing splines. J. Am. Stat. Assoc. 88, 1134–1143 (1988)
Peng, R., Welty, L.: The NMMAPSdata package. R News 4(2), 10–14 (2004)
Ramsay, J.: Monotone regression splines in action (with discussion). Stat. Sci. 3(4), 425–461 (1988)
Ruppert, D.: Selecting the number of knots for penalized splines. J. Comput. Graph. Stat. 11(4), 735–757 (2002)
Silverman, B.: Some aspects of the spline smoothing approach to nonparametric regression curve fitting. J. R. Stat. Soc.: Ser. B. 47, 1–52 (1985)
Shaddick, G., Choo, L., Walker, S.: Modelling correlated count data with covariates. J. Stat. Comput. Simul. 77(11), 945–954 (2007)
Villalobos, M., Wahba, G.: Inequality-constrained multivariate smoothing splines with application to the estimation of posterior probabilities. J. Am. Stat. Assoc. 82(397), 239–248 (1987)
Wahba, G.: Bayesian confidence intervals for the cross validated smoothing spline. J. R. Stat. Soc: Ser. B. 45, 133–150 (1983)
Wang, J., Meyer, M.: Testing the monotonicity or convexity of a function using regression splines. Can. J. Stat. 39(1), 89–107 (2011)
Wood, S.: Monotonic smoothing splines fitted by cross validation. SIAM J. Sci. Comput. 15(5), 1126–1133 (1994)
Wood, S.: Stable and efficient multiple smoothing parameter estimation for generalized additive models. J. Am. Stat. Assoc. 99, 673–686 (2004)
Wood, S.: On confidence intervals for generalized additive models based on penalized regression splines. Aust. N. Z. J. Stat. 48(4), 445–464 (2006b)
Wood, S.: Fast stable direct fitting and smoothness selection for generalized additive models. J. R. Stat. Soc. B 70(3), 495–518 (2008)
Wood, S.: Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models. J. R. Stat. Soc. B 73(1), 1–34 (2011)