Flexible smoothing with B-splines and penalties

Statistical Science - Tập 11 Số 2 - 1996
Paul H.C. Eilers, Brian D. Marx1
1Louisiana State University

Tóm tắt

Từ khóa


Tài liệu tham khảo

Silverman, B. W. (1986). Density Estimation for Statistics and Data Analy sis. Chapman and Hall, London.

Fan, J. and Gijbels, I. (1996). Local Poly nomial Modelling and its Applications. Chapman and Hall, London.

Hastie, T. and Tibshirani, R. (1990). Generalized Additive Models. Chapman and Hall, London.

Scott, D. W. (1992). Multivariate Density Estimation: Theory, Practice, and Visualization. Wiley, New York.

Eubank, R. L. (1988). Spline Smoothing and Nonparametric Regression. Dekker, New York.

Rice, J. (1984). Bandwidth choice for nonparametric regression. Ann. Statist. 12 1215-1230.

Fan, J. and Gijbels, I. (1995). Data-driven bandwidth selection in local poly nomial fitting: variable bandwidth and spatial adaptation. J. Roy. Statist. Soc. Ser. B 57 371-394.

Fan, J. and Marron, J. S. (1994). Fast implementations of nonparametric curve estimators. J. Comput. Graph. Statist. 3 35-56.

Fan, J. (1993). Local linear regression smoothers and their minimax efficiency. Ann. Statist. 21 196-216.

Mallows, C. (1973). Some comments on cp. Technometrics 15 661-675.

Wahba, G. (1990). Spline Models for Observational Data. SIAM, Philadelphia.

Kneip, A. (1994). Ordered linear smoothers. Ann. Statist. 22 835-866.

Hjort, N. L. and Jones, M. C. (1996). Locally parametric nonparametric density estimation. Ann. Statist. 24 1619-1647.

Ruppert, D., Sheather, S. J. and Wand, M. P. (1995). An effective bandwidth selector for local least squares regression. J. Amer. Statist. Assoc. 90 1257-1270.

Scott, D. W. and Terrell, G. R. (1987). Biased and unbiased cross-validation in density estimation. J. Amer. Statist. Assoc. 82 1131-1146.

McCullagh, P. and Nelder, J. A. (1989). Generalized Linear Models, 2nd ed. Chapman and Hall, London.

Green, P. J. and Silverman, B. W. (1994). Nonparametric Regression and Generalized Linear Models. Chapman and Hall, London.

Simonoff, J. S. (1996). Smoothing Methods in Statistics. Springer, New York.

Wahba, G. (1978). Improper priors, spline smoothing and the problem of guarding against model errors in regression. J. Roy. Statist. Soc. Ser. B 40 364-372.

Friedman, J. H. (1991). Multivariate adaptive regression splines (with discussion). Ann. Statist. 19 1-141.

KOOPERBERG, C. and STONE, C. J. (1991). A study of logspline density estimation. Comput. Statist. Data Anal. 12 327-347.

Green, P. J. and Yandell, B. S. (1985). Semi-parametric generalized linear models. In Generalized Linear Models (B. Gilchrist et al., eds.). Springer, New York. Hand, D. J., Daly, F., Lunn, A. D., McConway, K. J. and Ostrowski, E. (1994). A Handbook of Small Data Sets. Chapman and Hall, London.

Silverman, B. W. (1985). Some aspects of the spline smoothing approach to nonparametric regression curve fitting (with discussion). J. Roy. Statist. Soc. Ser. B 47 1-52.

Whittaker, E. T. (1923). On a new method of graduation. Proc. Edinburgh Math. Soc. 41 63-75.

Xiang, D. and Wahba, G. (1996). A generalized approximate cross validation for smoothing splines with non-Gaussian date. Statist. Sinica. To appear.

Ashford, R. and Walker, P. J. (1972). Quantal response analysis for a mixture of populations. Biometrics 28 981-988.

Bishop, Y. M. M., Fienberg, S. E. and Holland, P. W. (1975). Discrete Multivariate Analy sis: Theory and Practice. MIT Press.

Cleveland, W. S. (1979). Robust locally weighted regression and smoothing scatter plots. J. Amer. Statist. Assoc. 74 829-836.

Cox, M. G. (1981). Practical spline approximation. In Topics in Numerical Analy sis (P. R. Turner, ed.). Springer, Berlin.

de Boor, C. (1977). Package for calculating with B-splines. SIAM J. Numer. Anal. 14 441-472.

de Boor, C. (1978). A Practical Guide to Splines. Springer, Berlin.

Dierckx, P. (1993). Curve and Surface Fitting with Splines. Clarendon, Oxford.

Diggle P. and Marron J. S. (1988). Equivalence of smoothing parameter selectors in density and intensity estimation. J. Amer. Statist. Assoc. 83 793-800.

Eilers, P. H. C. (1990). Smoothing and interpolation with generalized linear models. Quaderni di Statistica e Matematica Applicata alle Scienze Economico-Sociali 12 21-32. Eilers, P. H. C. (1991a). Penalized regression in action: estimating pollution roses from daily averages. Environmetrics 2 25-48. Eilers, P. H. C. (1991b). Nonparametric density estimation with grouped observations. Statist. Neerlandica 45 255-270.

Eilers, P. H. C. (1995). Indirect observations, composite link models and penalized likelihood. In Statistical Modelling (G. U. H. Seeber et al., eds.). Springer, New York.

Eilers, P. H. C. and Marx, B. D. (1992). Generalized linear models with P-splines. In Advances in GLIM and Statistical Modelling (L. Fahrmeir et al., eds.). Springer, New York.

Friedman, J. and Silverman, B. W. (1989). Flexible parsimonious smoothing and additive modeling (with discussion). Technometrics 31 3-39.

Hardle, W. (1990). Applied Nonparametric Regression. Cambridge Univ. Press.

Kooperberg, C. and Stone, C. J. (1992). Logspline density estimation for censored data. J. Comput. Graph. Statist. 1 301- 328.

Marron, J. S. and Ruppert, D. (1994). Transformations to reduce boundary bias in kernel density estimation. J. Roy. Statist. Soc. Ser. B 56 653-671.

Marx, B. D. and Eilers, P. H. C. (1994). Direct generalized additive modelling with penalized likelihood. Paper presented at the 9th Workshop on Statistical Modelling, Exeter, 1994.

Marx, B. D. and Eilers, P. H. C. (1996). Direct generalized additive modelling with penalized likelihood. Unpublished manuscript.

O'Sullivan, F. (1986). A statistical perspective on ill-posed inverse problems (with discussion). Statist. Sci. 1 505-527.

O'Sullivan, F. (1988). Fast computation of fully automated logdensity and log-hazard estimators. SIAM J. Sci. Statist. Comput. 9 363-379.

Reinsch, C. (1967). Smoothing by spline functions. Numer. Math. 10 177-183.

Sakamoto, Y., Ishiguro, M. and Kitagawa, G. (1986). Akaike Information Criterion Statistics. Reidel, Dordrecht.

Wand, M. P. and Jones, M. C. (1993). Kernel Smoothing. Chapman and Hall, London.

Chiu, S.-T. (1996). A comparative review of bandwidth selection for kernel density estimation. Statist. Sinica 6 129-145.

Hall, P. and Johnstone, I. (1992). Empirical functionals and efficient smoothing parameter selection. J. Roy. Statist. Soc. Ser. B 54 519-521.

Hall, P., Marron, J. S. and Park, B. U. (1992). Smoothed crossvalidation. Probab. Theory Related Fields 92 1-20.

Barry, D. (1993). Testing for additivity of a regression function. Ann. Statist. 21 235-254.

Cox, D. D. and Chang, Y.-F. (1990). Iterated state space algorithms and cross validation for generalized smoothing splines. Technical Report 49, Dept. Statistics, Univ. Illinois.

Cox, D. D., Koh, E., Wahba, G. and Yandell, B. S. (1988). Testing the (parametric) null model hy pothesis in (semiparametric) partial and generalized spline models. Ann. Statist. 16 113-119.

Gu, C. (1992). Cross validating non Gaussian data. Journal of Computational and Graphical Statistics 1 169-179.

Gu, C. (1996). Model indexing and smoothing parameter selection in nonparametric function estimation. Technical Report 93-55 (rev.), Dept. Statistics, Purdue Univ.

Wahba, G. (1983). Bayesian "confidence intervals" for the crossvalidated smoothing spline. J. Roy. Statist. Soc. Ser. B 45 133-150.

Ansley, C. F., Kohn, R. and Wong, C. M. (1993). Nonparametric spline regression with prior information. Biometrika 80 75- 88.

Efron, B. and Tibshirani, R. (1996). Using specially designed exponential families for density estimation. Ann. Statist. 24 000-000.

Hjort, N. L. (1996). Performance of Efron and Tibshirani's semiparametric denisty estimator. Unpublished manuscript.

Jones, M. C. (1991). On correcting for variance inflation in kernel density estimation. Comput. Statist. Data Anal. 11 3-15.

Jones, M. C. (1996). On close relations of local likelihood density estimation. Unpublished manuscript.

Loader, C. R. (1996). Local likelihood density estimation. Ann. Statist. 24 1602-1618

Marron, J. S. (1996). A personal view of smoothing and statistics (with discussion). Comput. Statist. To appear.

Cook, R. D. and Weisberg, S. (1994). Regression Graphics. Wiley, New York.

Eilers, P. H. C. (1988). Autoregressive models with latent variables. In COMPSTAT 1988 Proceedings (D. Edwards and N. E. Raun, eds.). physica-Verlag.

Engel, J. and Gasser, T. (1995). A minimax result for a class of nonparametric density estimators. Nonparametric Statistics 4 327-334.

Fan, J., Hall, P., Martin, M. A. and Patil, P. (1996). On local smoothing of nonparametric curve estimators. J. Amer. Statist. Assoc. 91 258-266. Foley, J. D., van Dam, A., Feiner, S. K. and Hughes, J. F.

Jones, M. C., Marron, J. S. and Sheather, S. J. (1996). A brief survey of bandwidth selection for density estimation. J. Amer. Statist. Assoc. To appear.

Kooperberg, C., Bose, S. and Stone, C. J. (1997). Poly chotomous regression. J. Amer. Statist. Assoc. To appear. Kooperberg, C., Stone, C. J. and Truong, Y. K. (1995a). Hazard regression. J. Amer. Statist. Assoc. 90 78-94. Kooperberg, C., Stone, C. J. and Truong, Y. K. (1995b). Logspline estimation of a possibly mixed spectral distribution. J. Time Ser. Anal. 16 359-388.

Speckman, P. L. (1983). Spline smoothing and optimal rates of convergence in nonparametric regression models. Ann. Statist. 13 970-983. Stone, C. J., Hansen, M., Kooperberg, C. and Truong, Y. K.