Tobit model estimation and sliced inverse regression

Statistical Modelling

Volumn 7, Issue 2, 2007, Pages 107-123

  Li, Lexin ^a   Simonoff, Jeffrey S ^b   Tsai, Chih Ling ^c  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

^b NEW YORK UNIVERSITY   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Dimension reduction; Heteroscedasticity; Nonnormality; Single index model

Indexed keywords

EID: 34848875663     PISSN: 1471082X     EISSN: 14770342     Source Type: Journal    
DOI: 10.1177/1471082X0700700201     Document Type: Article

References (34)

1. Amemiya T (1973) Regression analysis when the dependent variable is truncated normal. Econometrica, 41, 997-1016.
2. Amemiya T (1984) Tobit models: a survey. Journal of Econometrics, 24, 3-61.
3. Arabmazar A and Schmidt P (1981) Further evidence on the robustness of the Tobit estimator to heteroscedasticity. Journal of Econometrics, 17, 253-58.
4. Arabmazar A and Schmidt P (1982) An investigation of the robustness of the Tobit estimator to non-normality. Econometrica, 50, 1055-63.
5. Buckley J and James I (1979) Linear regression with censored data. Biometrika, 66, 429-36.
6. Carroll RJ and Li KC (1995) Binary regressors in dimension reduction models: A new look at treatment comparisons. Statistica Sinica, 5, 667-88.
7. Chen CH and Li KC (1998) Can SIR be as popular as multiple linear regression? Statistica Sinica, 8, 289-316.
8. Chernozhukov V and Hong H (2002) Three-step censored quantile regression and extramarital affairs. Journal of the American Statistical Association, 97, 872-82.
9. Chiaromonte F, Cook RD and Li B (2002) Sufficient dimension reduction in regressions with categorical predictors. Annals of Statistics, 30, 475-97.
10. Cook RD (1994) On the interpretation of regression plots. Journal of the American Statistical Association, 89, 177-90.
11. Cook RD (1998) Regression Graphics: Ideas for Studying Regressions Through Graphics. New York: Wiley.
12. Cook RD (2003) Dimension reduction and graphical exploration in regression including survival analysis. Statistics in Medicine, 22, 1399-413.
13. Cook RD and Li B (2002) Dimension reduction for the conditional mean in regression. Annals of Statistics, 30, 455-74.
14. Cook RD and Nachtsheim CJ (1994) Re-weighting to achieve elliptically contoured covariates in regression. Journal of the American Statistical Association, 89, 592-600.
15. Cook RD and Ni L (2005) Sufficient dimension reduction via inverse regression: a minimum discrepancy approach. Journal of the American Statistical Association, 100, 410-28.
16. Cook RD and Weisberg S (1991) Discussion of Li (1991). Journal of American Statistical Association, 86, 328-32.
17. Eaton M (1986) A characterization of spherical distributions. Journal of Multivariate Analysis, 20, 272-76.
18. Efron B (1979) Bootstrap methods: Another look at the jackknife. Annals of Statistics, 7, 1-26.
19. Fitzenberger B (1997) Computational aspects of censored quantile regression. In Dodge Y ed. Proceedings of the 3rd International Conference on Statistical Data Analysis Based on the L1-Norm and Related Methods. Hayward, CA: Institute of Mathematical Statistics, 171-86.
20. Goldberger AS (1980) Abnormal selection bias. SSRI Workshop Series no. 8006. University of Wisconsin, Madison.
21. Hall P and Li KC (1993) On almost linearity of low dimensional projections from high dimensional data. Annals of Statistics, 21, 867-89.
22. Heller G and Simonoff JS (1990) A comparison of estimators for regression with a censored response variable. Biometrika, 77, 515-20.
23. Li KC (1991) Sliced inverse regression for dimension reduction (with discussion). Journal of the American Statistical Association, 86, 316-27.
24. Li KC (1992) On principal Hessian directions for data visualization and dimension reduction: another application of Stein's Lemma. Annals of Statistics, 87, 1025-39.
25. Li KC, Wang JL and Chen CH (1999) Dimension reduction for censored regression data. Annals of Statistics, 27, 1-23.
26. Li L, Cook RD and Nachtsheim CJ (2004) Cluster-based estimation for sufficient dimension reduction. Computational Statistics and Data Analysis, 47, 175-93.
27. Naik P and Tsai CL (2000) Partial least squares estimator for single-index models. Journal of the Royal Statistical Society, Series B, 62, 763-71.
28. Powell JL (1984) Least absolute deviations estimation for the censored regression model. Journal of Econometrics, 25, 303-25.
29. Powell JL, Stock JH and Stoker TM (1989) Semiparametric estimation of index coefficients. Econometrica, 57, 1403-30.
30. Simonoff JS (1996) Smoothing Methods in Statistics. New York: Springer-Verlag.
31. Smith DA and Brame R (2003) Tobit models in social science research: Some limitations and a more general alternative. Sociological Methods and Research, 31, 364-88.
32. Tobin J (1958) Estimation of relationships for limited dependent variables. Econometrica, 26, 24-36.
33. Yen ST (2002) An econometric analysis of household donations in the USA. Applied Economics Letters, 9, 837-41.
34. Zhu LX and Ng KW (1995) Asymptotics of sliced inverse regression. Statistica Sinica, 5, 727-36.