Conditional transformation models

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 76, Issue 1, 2014, Pages 3-27

  Hothorn, Torsten ^a,b   Kneib, Thomas ^c   Bühlmann, Peter ^d  

^a UNIVERSITY OF MUNICH   (Germany)

^b UNIVERSITY OF ZURICH   (Switzerland)

^c UNIVERSITY OF GÖTTINGEN   (Germany)

^d ETH ZURICH   (Switzerland)

Author keywords

Boosting; Conditional distribution function; Conditional quantile function; Continuous ranked probability score; Prediction intervals; Structured additive regression

Indexed keywords

EID: 84891832147     PISSN: 13697412     EISSN: 14679868     Source Type: Journal    
DOI: 10.1111/rssb.12017     Document Type: Article

References (56)

1. Bühlmann, P. (2006) Boosting for high-dimensional linear models. Ann. Statist., 34, 559-583.
2. Bühlmann, P. and van de Geer, S. (2011) Statistics for High-dimensional Data: Methods, Theory and Applications. Berlin: Springer.
3. Bühlmann, P. and Hothorn, T. (2007) Boosting algorithms: regularization, prediction and model fitting (with discussion). Statist. Sci., 22, 477-505.
4. Bühlmann, P. and Yu, B. (2003) Boosting with the L2 loss: regression and classification. J. Am. Statist. Ass., 98, 324-339.
5. Chen, K. and Müller, H. G. (2012) Conditional quantile analysis when covariates are functions, with application to growth data. J. R. Statist. Soc. B, 74, 67-89.
6. Chen, K. and Tong, X. (2010) Varying coefficient transformation models with censored data. Biometrika, 97, 969-976.
7. Cheng, G. and Wang, X. (2011) Semiparametric additive transformation model under current status data. Electron. J. Statist., 5, 1735-1764.
8. Cheng, S. C., Wei, L. J. and Ying, Z. (1995) Analysis of transformation models with censored data. Biometrika, 82, 835-845.
9. Currie, I. D., Durban, M. and Eilers, P. H. C. (2006) Generalized linear array models with applications to multidimensional smoothing. J. R. Statist. Soc. B, 68, 259-280.
10. Dette, H. and Volgushev, S. (2008) Non-crossing non-parametric estimates of quantile curves. J. R. Statist. Soc. B, 70, 609-627.
11. Doksum, K. A. and Gasko, M. (1990) On a correspondence between models in binary regression analysis and in survival analysis. Int. Statist. Rev., 58, 243-252.
12. Eilers, P. H. C. (2005) Unimodal smoothing. J. Chemometr., 19, 317-328.
13. Fenske, N., Kneib, T. and Hothorn, T. (2011) Identifying risk factors for severe childhood malnutrition by boosting additive quantile regression. J. Am. Statist. Ass., 106, 494-510.
14. Friedman, H. H., Friedman, L. W. and Amoo, T. (2002) Using humor in the introductory statistics course. J. Statist. Educ., 10, no. 3.
15. van de Geer, S. (2000) Empirical Processes in M-estimation. Cambridge: Cambridge University Press.
16. Gilchrist, W. (2008) Regression revisited. Int. Statist. Rev., 76, 401-418.
17. Gneiting, T. and Raftery, A. E. (2007) Strictly proper scoring rules, prediction, and estimation. J. Am. Statist. Ass., 102, 359-378.
18. Gneiting, T., Raftery, A. E., Westveld III, A. H. and Goldman, T. (2005) Calibrated probabilistic forecasting using ensemble model output statistics and minimum CRPS estimation. Mnthly Weath. Rev., 133, 1098-1118.
19. Gneiting, T. and Ranjan, R. (2011) Comparing density forecasts using threshold- and quantile-weighted scoring rules. J. Bus. Econ. Statist., 29, 411-422.
20. Hall, P. and Müller, H. G. (2003) Order-preserving nonparametric regression, with applications to conditional distribution and quantile function estimation. J. Am. Statist. Ass., 98, 598-608.
21. Hall, P., Wolff, R. C. L. and Yao, Q. (1999) Methods for estimating a conditional distribution function. J. Am. Statist. Ass., 94, 154-163.
22. Hayfield, T. and Racine, J. S. (2008) Nonparametric econometrics: the np package. J. Statist. Softwr., 27, 1-32.
23. Hayfield, T. and Racine, J. S. (2011) np: nonparametric kernel smoothing methods for mixed data types. R Package Version 0.40-12. (Available from http://CRAN.Rproject.org/package=np.)
24. He, X. (1997) Quantile curves without crossing. Am. Statistn, 51, 186-192.
25. Hofner, B., Hothorn, T., Kneib, T. and Schmid, M. (2011a) A framework for unbiased model selection based on boosting. J. Computnl Graph. Statist., 20, 956-971.
26. Hofner, B., Mayr, A., Fenske, N. and Schmid, M. (2011b) gamboostLSS: boosting methods for GAMLSS models. R Package Version 1.0-3/r39. (Available from http://Rforge.Rproject.org/projects/gamboostlss/.)
27. Hothorn, T., Bühlmann, P., Dudoit, S., Molinaro, A. and van der Laan, M. J. (2006) Survival ensembles. Biostatistics, 7, 355-373.
28. Hothorn, T., Bühlmann, P., Kneib, T., Schmid, M. and Hofner, B.(2011) mboost: model-based boosting. R Package Version 2.1-1. (Available from http://CRAN.Rproject.org/package=mboost.)
29. Hothorn, T., Kneib, T. and Bühlmann, P. (2012) Conditional transformation models (extended version). Technical Report arXiv:1201.5786v2. Ludwig-Maximilians-Universität München, Munich. (Available from http://arxiv.org/abs/1201.5786.)
30. International Institute for Population Sciences and ORC Macro (2000) National Family Health Survey (NFHS-2), 1998-1999: India. International Institute for Population Sciences, Mumbai. (Available from http://www.measuredhs.com/pubs.)
31. Koenker, R. (2005) Quantile Regression. New York: Cambridge University Press.
32. Koenker, R. (2011) quantreg: quantile regression. R Package Version 4.76. (Available from http://CRAN.Rproject.org/package=quantreg.)
33. Koenker, R. and Bassett, G. (1978) Regression quantiles. Econometrica, 46, 33-50.
34. Koenker, R., Ng, P. and Portnoy, S. (1994) Quantile smoothing splines. Biometrika, 81, 673-680.
35. Kriegler, B. and Berk, R. (2010) Small area estimation of the homeless in Los Angeles: an application of cost-sensitive stochastic gradient boosting. Ann. Appl. Statist., 4, 1234-1255.
36. Li, Q. and Racine, J. S. (2008) Nonparametric estimation of conditional CDF and quantile functions with mixed categorical and continuous data. J. Bus. Econ. Statist., 26, 423-434.
37. Lu, W. and Li, L. (2008) Boosting method for nonlinear transformation models with censored survival data. Biostatistics, 9, 658-667.
38. Lu, W. and Zhang, H. H. (2010) On estimation of partially linear transformation models. J. Am. Statist. Ass., 105, 683-691.
39. Mayr, A., Fenske, N., Hofner, B., Kneib, T. and Schmid, M. (2012a) Generalized additive models for location, scale and shape for high dimensional data-a flexible approach based on boosting. Appl. Statist., 61, 403-427.
40. Mayr, A., Hothorn, T. and Fenske, N. (2012b) Prediction intervals for future BMI values of individual children-a non-parametric approach by quantile boosting. BMC Med. Res. Methodol., 12, article 6.
41. R Development Core Team (2011) R: a Language and Environment for Statistical Computing. Vienna: R Foundation for Statistical Computing.
42. Ridgeway, G. (2002) Looking for lumps: boosting and bagging for density estimation. Computnl Statist. Data Anal., 38, 379-392.
43. Rigby, R. A. and Stasinopoulos, D. M. (2005) Generalized additive models for location, scale and shape (with discussion). Appl. Statist., 54, 507-554.
44. Schemper, M. and Henderson, R. (2000) Predictive accuracy and explained variation in Cox regression. Biometrics, 56, 249-255.
45. Schild, R. L., Maringa, M., Siemer, J., Meurer, B., Hart, N., Goecke, T. W., Schmid, M., Hothorn, T. and Hansmann, M. E. (2008) Weight estimation by three-dimensional ultrasound imaging in the small fetus. Ultrasnd Obstetr. Gyn., 32, 168-175.
46. Schmid, M. and Hothorn, T. (2008) Flexible boosting of accelerated failure time models. BMC Bioinform., 9, article 269.
47. Schmid, M., Hothorn, T., Maloney, K. O., Weller, D. E. and Potapov, S. (2011) Geoadditive regression modeling of stream biological condition. Environ. Ecol. Statist., 18, 709-733.
48. Schnabel, S. K. and Eilers, P. H. C. (2012) Simultaneous estimation of quantile curves using quantile sheets. AStA Adv. Statist. Anal., to be published, doi 10.1007/s10182-012-0198-1.
49. Sexton, J. and Laake, P. (2012) Boosted coefficient models. Statist. Comput., 22, 867-876.
50. Shen, X. (1998) Proportional odds regression and sieve maximum likelihood estimation. Biometrika, 85, 165-177.
51. Stasinopoulos, M., Rigby, B. and Akantziliotou, C. (2011) gamlss: generalized additive models for location scale and shape. R Package Version 4.1-1. (Available from http://CRAN.Rproject.org/package=gamlss.)
52. Tutz, G. and Groll, A. (2012) Likelihood-based boosting in binary and ordinal random effects models. J. Computnl Graph. Statist., to be published, doi 10.1080/10618600.2012.694769.
53. Tutz, G. and Petry, S. (2012) Nonparametric estimation of the link function including variable selection. Statist. Comput., 22, 545-561.
54. Wu, C., Tian, X. and Yu, J. (2010) Nonparametric estimation for time-varying transformation models with longitudinal data. J. Nonparam. Statist., 22, 133-147.
55. Zeng, D., Lin, D. Y. and Yin, G. (2005) Maximum likelihood estimation for the proportional odds model with random effects. J. Am. Statist. Ass., 100, 470-483.
56. Zheng, S. (2012) QBoost: predicting quantiles with boosting for regression and binary classiffication. Exprt Syst. Applic., 39, 1687-1697.