Nonparametric n-1/2-consistent estimation for the general tranformation models

Annals of Statistics

Volumn 25, Issue 6, 1997, Pages 2682-2717

  Ye, Jianming ^a   Duan, Naihua ^b  

^a UNIVERSITY OF CHICAGO   (United States)

^b RAND CORPORATION   (United States)

Author keywords

Primary 62G07; Secondary 62G02

Indexed keywords

EID: 0031326926     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. BAHADUR, R. R. (1966). A note on quantiles in large samples. Ann. Math. Statist. 37 577-580.
2. BICKEL, P. J. and DOKSUM, K. A. (1981). An analysis of transformations revisited. J. Amer. Statist. Assoc. 76 296-311.
3. Box, G. E. P. and Cox, D. R. (1964). An analysis of transformations (with discussion). J. Roy. Statist. Soc. Ser B 26 211-252.
4. Box, G. E. P. and Cox, D. R. (1982). Comment on "An analysis of transformations revisited," by P. J. Bickel and K. A. Doksum. J. Amer. Statist. Assoc. 77 209-210.
5. BREIMAN, L. and FRIEDMAN, J. H. (1985). Estimating optimal transformations for multiple regression and correlation, J. Amer. Statist. Assoc. 80 580-598.
6. CARROLL, R. J. and RUPPERT, D. (1988). Transformation and Weighting in Regression. Chapman and Hall, London.
7. CHAUDHURI, P., DOKSUM, K. and SAMAROV, A. (1994). Nonparametric estimation of global functionals based on quantile regression. Unpublished manuscript.
8. DOKSUM, K. (1987). An extension of partial likelihood methods for proportional hazard models to general transformation models. Ann. Statist. 15 325-345.
9. DUAN, N. (1990). The adjoint projection pursuit regression. J. Amer. Statist. Assoc. 85 1029-1038.
10. EFRON, B. (1982). Transformation theory: how normal is a family of distributions? Ann. Statist. 10 323-339.
11. FRIEDMAN, J. H. and STUETZLE, W. (1981). Projection pursuit regression. J. Amer. Statist. Assoc. 76 817-823.
12. HÄRDLE, W. and STOKER, T. (1989). Investigating smooth multiple regression by the method of average derivatives. J. Amer. Statist. Assoc. 84 986-995.
13. HECKMAN, J. and SINGER, B. (1984). A method for minimizing the impact of distributional assumptions in econometric models for duration data. Econometrica 52 271-320.
14. HINKLEY, D. V. and RUNGER, G. (1984). The analysis of transformed data (with discussion). J. Amer. Statist. Assoc. 79 302-320.
15. HOROWITZ, J. L. (1996). Semiparametric estimation of a regression model with an unknown transformation of the dependent variable. Econometrica 64 103-137.
16. KRUSKAL, J. B. (1965). Analysis of factorial experiments by estimating monotone transformations of the data. J. Roy. Statist. Soc. Ser. B 27 251-263.
17. MURPHY, S. A. (1994). Consistency in a proportional hazards model incorporating a random effect. Ann. Statist. 22 712-731.
18. MURPHY, S. A. (1995). Asymptotic theory for the frailty model. Ann. Statist. 23 182-198.
19. PAKES, A. and POLLARD, D. (1989). Simulation and the asymptotics of optimization estimators. Econometrica 57 1027-1057.
20. POLLARD, D. (1984). Convergence, of Stochastic Processes. Springer, New York.
21. SERFLING, R. (1980). Approximation Theorems of Mathematical Statistics. Wiley, New York.
22. SHEN, X. (1997). On methods of sieves and penalization. Ann. Statist. 25 2555-2591.
23. WANG, N. and RUPPERT, D. (1995). Nonparametric estimation of the transformation in the transformation-both-sides regression model. J. Amer. Statist. Assoc. 90 522-584.
24. WANG, N. and RUPPERT, D. (1996). Estimation of regression parameters in a semiparametric transformation model. J. Statist. Plann. Inference 52 331-351.