Estimation of a semiparametric transformation model

Annals of Statistics

Volumn 36, Issue 2, 2008, Pages 686-718

  Linton, Oliver ^a   Sperlich, Stefan ^b   Van Keilegom, Ingrid ^c  

^a LONDON SCHOOL OF ECONOMICS   (United Kingdom)

^b UNIVERSITY OF GÖTTINGEN   (Germany)

^c UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

Author keywords

Additive models; Generalized structured models; Profile likelihood; Semiparametric models; Separability; Transformation models

Indexed keywords

EID: 51049124284     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053607000000848     Document Type: Article

References (41)

1. AMEMIYA. T. and POWELL, J. L. (1981). A comparison of the Box-Cox maximum likelihood estimator and the nonlinear two-stage least squares estimator. J. Econometrics17351-381. MR0659799
2. BICKEL, P. J. and DORSUM, K. (1981). An analysis of transformations revisited. J. Amer. Statist. Assoc. 76 296-311. MR0624332
3. BOX, G. E. P. and COX. D. R. (1964). An analysis of transformations. J. Roy. Statist. Soc. Ser. B 26 211-252. MR0192611
4. BREIMAN, L. and FRIEDMAN, J. H. (1985). Estimating optimal transformations for multiple regression and correlation (with discussion). J. Amer. Statist. Assoc. 80 580-619. MR0803258
5. CARROLL, R. J. and RUPPERT, D. (1984). Power transformation when fitting theoretical models to data. J. Amer. Statist. Assoc. 79 321-328. MR0755088
6. CARROLL, R. J. and RUPPERT, D. (1988). Transformation and Weighting in Regression. Chapman and Hall, New York. MR1014890
7. CHEN, X., LINTON, O. B. and VAN KEILEGOM. I. (2003). Estimation of semiparametric models when the criterion function is not smooth. Econometrica 71 1591-1608. MR2000259
8. CHENG, S. C., WEI. L. J. and YING, Z. (1995). Analysis of transformation models with censored data. Biometrika 82 835-845. MR 1380818
9. CHENG, K. F. and WU, J. W. (1994). Adjusted least squares estimates for the scaled regression coefficients with censored data. J. Amer. Statist. Assoc. 89 1483-1491. MR1310237
10. DOKSUM, K. (1987). An extension of partial likelihood methods for proportional hazard models to general transformation models. Ann. Statist. 15 325-345. MR0885740
11. EKELAND. I., HECKMAN, J. J. and NESHEIM, L. (2004). Identification and estimation of Hedonic Models. J. Political Economy112S60-S109.
12. HALL, P. and HOROWITZ, J. L. (1996). Bootstrap critical values for tests based on generalized-method-of-moments estimators. Econometrica 64 891-916. MR1399222
13. HENGARTNER, N. W. and SPERLICH. S. (2005). Rate optimal estimation with the integration method in the presence of many covariates. J. Multivariate Anal. 95 246-272. MR2170397
14. HOROWITZ, J. (1996). Semiparametric estimation of a regression model with an unknown transformation of the dependent variable. Econometrica 64 103-137. MR1366143
15. HOROWITZ, J. (2001). Nonparametric estimation of a generalized additive model with an unknown link function. Econometrica 69 499-513. MR1819761
16. IBRAGIMOV, I. A. and HASMINSKII, R. Z. (1980). On nonparametric estimation of regression. Soviet Math. Dokl. 21 810-814.
17. JOHNSON, N. L. (1949). Systems of frequency curves generated by methods of translation. Biometrika 36 149-176. MR0033994
18. KOUL. H. L. (2001). Weighted Empirical Processes in Regression and Autoregression Models. Springer, New York.
19. LEWBEL, A. and LINTON, O. (2007). Nonparametric matching and efficient estimators of homo-thetically separable functions. Econometrica 75 1209-1227.
20. LINTON, O. B.. CHEN, R., WANG, N. and HÄRDLE, W. (1997). An analysis of transformations for additive nonparametric regression. J. Amer. Statist. Assoc. 92 1512-1521. MR1615261
21. LINTON. O. and MAMMEN, E. (2005). Estimating semiparametric ARCH(∞) models by kernel smoothing. Econometrica73771-836. MR2135143
22. LINTON, O. B. and NIELSEN, J. P. (1995). A kernel method of estimating structured nonparametric regression using marginal integration. Biometrika 82 93-100. MR1332841
23. MAMMEN, E., LINTON. O. B. and NIELSEN. J. P. (1999). The existence and asymptotic properties of a backfitting projection algorithm under weak conditions. Ann. Statist. 27 1443-1490. MR1742496
24. MAMMEN, E. and PARK. B. U. (2005). Bandwidth selection for smooth backfitting in additive models. Ann. Statist. 33 1260-1294. MR2195635
25. NIELSEN. J. P., LINTON, O. B. and BICKEL, P. J. (1998). On a semiparametric survival model with flexible covariate effect. Ann. Statist.26215-241. MR1611784
26. NIELSEN, J. P. and SPERLICH, S. (2005). Smooth backfitting in practice. J. Roy. Statist. Soc. Ser. B 61 43-61. MR2136638
27. ROBINSON. P. M. (1991). Best nonlinear three-stage least squares estimation of certain econometric models. Econometrica59755-786. MR1106511
28. SEVERINI, T. A. and WONG. W. H. (1992). Profile likelihood and conditionally parametric models. Ann. Statist. 20 1768-1802. MR1193312
29. SPERLICH. S. (2005). On nonparametric estimation with constructed variables and generated regressors. Preprint, Univ. Carlos III de Madrid, Spain.
30. SPERLICH, S., LINTON, O. B. and HÄRDLE, W. (1999). Integration and backfitting methods in additive models: Finite sample properties and comparison. Test 8 419-458.
31. SPERLICH, S.. LINTON, O. B. and VAN KEILEGOM, I. (2007). A computational note on estimation of a semiparametric transformation model. Preprint, Georg-August Univ. Göttingen, Germany.
32. SPERLICH, S.. TJØSTHEIM, D. and YANG, L. (2002). Nonparametric estimation and testing of interaction in additive models. Econometric Theory 18 197-251. MR 1891823
33. STONE, C. J. (1980). Optimal rates of convergence for nonparametric estimators. Ann. Statist. 8 1348-1360. MR0594650
34. STONE, C.J. (1982). Optimal global rates of convergence for nonparametric regression. Ann. Statist. 10 1040-1053. MR0673642
35. STONE, C. J. (1986). The dimensionality reduction principle for generalized additive models. Ann. Statist. 14 592-606. MR0840516
36. TJØSTHEIM, D. and AUESTAD, B. (1994). Nonparametric identification of nonlinear time series: Projections. J. Amer. Statist. Assoc. 89 1398-1409. MR1310230
37. VAN DEN BERG, G. J. (2001). Duration models: Specification, identification and multiple durations. In The Handbook of Econometrics V (J. J. Heckman and E. Learner, eds.) 3381-3460. North-Holland. Amsterdam.
38. VAN DER VAART, A. W. and WELLNER, J. A. (1996). Weak Convergence and Empirical Processes. Springer, New York. MR1385671
39. VAN KEILEGOM, I. and VERAVERBEKE, N. (2002). Density and hazard estimation in censored regression models. Bernoulli 8 607-625. MR1935649
40. WEI, L. J. (1992). The accelerated failure time model: A useful alternative to the Cox regression model in survival analysis. Statistics in Medicine 11 1871-1879.
41. ZELLNER. A. and REVANKAR, N. S. (1969). Generalized production functions. Rev. Economic Studies36241-250.