| conquer-package {conquer} | R Documentation |
Estimation and inference for conditional linear quantile regression models using a convolution smoothed approach. In the low-dimensional setting, efficient gradient-based methods are employed for fitting both a single model and a regression process over a quantile range. Normal-based and (multiplier) bootstrap confidence intervals for all slope coefficients are constructed. In high dimensions, the conquer methods complemented with \ell_1-penalization and iteratively reweighted \ell_1-penalization are used to fit sparse models.
Xuming He <xmhe@umich.edu>, Xiaoou Pan <xip024@ucsd.edu>, Kean Ming Tan <keanming@umich.edu>, and Wen-Xin Zhou <wez243@ucsd.edu>
Barzilai, J. and Borwein, J. M. (1988). Two-point step size gradient methods. IMA J. Numer. Anal. 8 141–148.
Belloni, A. and Chernozhukov, V. (2011). \ell_1 penalized quantile regression in high-dimensional sparse models. Ann. Statist. 39 82-130.
Fan, J., Liu, H., Sun, Q. and Zhang, T. (2018). I-LAMM for sparse learning: Simultaneous control of algorithmic complexity and statistical error. Ann. Statist. 46 814-841.
Fernandes, M., Guerre, E. and Horta, E. (2019). Smoothing quantile regressions. J. Bus. Econ. Statist. 39 338-357.
He, X., Pan, X., Tan, K. M., and Zhou, W.-X. (2021+). Smoothed quantile regression for large-scale inference. J. Econometrics, in press.
Horowitz, J. L. (1998). Bootstrap methods for median regression models. Econometrica 66 1327–1351.
Koenker, R. (2005). Quantile Regression. Cambridge University Press, Cambridge.
Koenker, R. Package "quantreg".
Koenker, R. and Bassett, G. (1978). Regression quantiles. Econometrica 46 33-50.
Tan, K. M., Wang, L. and Zhou, W.-X. (2021+). High-dimensional quantile regression: convolution smoothing and concave regularization. J. Roy. Statist. Soc. Ser. B, in press.