The function conducts Huber regression from a data sample, with robustification parameter \(\tau\) determined by a tuning-free principle.
Usage
huber.reg(X, Y, method = c("standard", "adaptive"))
Arguments
X
An \(n\) by \(p\) design matrix, where \(p < n\).
Y
A continuous response with length \(n\).
method
An optional character string specifying the method to calibrate the robustification parameter \(\tau\). Two choices are "standard"(default) and "adaptive". See Wang et al.(2020) for details.
Value
A coefficients estimator with length \(p + 1\) will be returned.
References
Huber, P. J. (1964). Robust estimation of a location parameter. Ann. Math. Statist., 35, 73<U+2013>101.
Sun, Q., Zhou, W.-X. and Fan, J. (2020). Adaptive Huber regression. J. Amer. Statist. Assoc., 115, 254-265.
Wang, L., Zheng, C., Zhou, W. and Zhou, W.-X. (2020). A new principle for tuning-free Huber regression. Stat. Sin., to appear.
See Also
huber.mean for tuning-free Huber mean estimation and huber.cov for tuning-free Huber-type covariance estimation.