Smoothed rank correlation of the linear transformation regression model
The maximum rank correlation (MRC) approach is the most common method used in the literature to estimate the regression coefficients in the semiparametric linear transformation regression model. However, the objective function Gn(β) in the MRC approach is not continuous. The optimization of Gn(β) requires an extensive search for which the computational cost grows in the order of nd, where d is the dimension of X. Given the lack of smoothing, issues related to variable selection, the variance estimate and other inferences by MRC are not well developed in the model. In this paper, we combine the concept underlying the penalized method, rank correlation and smoothing technique and propose a nonconcave penalized smoothed rank correlation method to select variables and estimate parameters for the semiparametric linear transformation model. The proposed estimator is computationally simple, n1/2−consistent and asymptotically normal. A sandwich formula is proposed to estimate the variances of the proposed estimates. We also illustrate the usefulness of the methodology with real data from a body fat prediction study.
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- Han, Aaron K., 1987. "Non-parametric analysis of a generalized regression model : The maximum rank correlation estimator," Journal of Econometrics, Elsevier, vol. 35(2-3), pages 303-316, July.
- Hansheng Wang & Runze Li & Chih-Ling Tsai, 2007. "Tuning parameter selectors for the smoothly clipped absolute deviation method," Biometrika, Biometrika Trust, vol. 94(3), pages 553-568.
- Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320.
- Tue Gorgens & Joel L. Horowitz, 1996.
"Semiparametric Estimation of a Censored Regression Model with an Unknown Transformation of the Dependent Variable,"
- Gorgens, Tue & Horowitz, Joel L., 1999. "Semiparametric estimation of a censored regression model with an unknown transformation of the dependent variable," Journal of Econometrics, Elsevier, vol. 90(2), pages 155-191, June.
- Horowitz, J. & Gorgens, T., 1995. "Semiparametric Estimation of a Censored Regression Model with an Unknown Transformation of the Dependent Variable," Working Papers 95-15, University of Iowa, Department of Economics.
- Horowitz, Joel L, 1996. "Semiparametric Estimation of a Regression Model with an Unknown Transformation of the Dependent Variable," Econometrica, Econometric Society, vol. 64(1), pages 103-37, January.
- Sherman, Robert P, 1993. "The Limiting Distribution of the Maximum Rank Correlation Estimator," Econometrica, Econometric Society, vol. 61(1), pages 123-37, January.
- Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768.
- Kani Chen, 2002. "Semiparametric analysis of transformation models with censored data," Biometrika, Biometrika Trust, vol. 89(3), pages 659-668, August.
- Songnian Chen, 2002. "Rank Estimation of Transformation Models," Econometrica, Econometric Society, vol. 70(4), pages 1683-1697, July.
- Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
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