huber.reg {FarmTest}

Tuning-free Huber regression

Description

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, 73–101.

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.

Examples

n = 200
d = 10
beta = rep(1, d)
X = matrix(rnorm(n * d), n, d)
err = rnorm(n)
Y = 1 + X %*% beta + err
beta.hat = huber.reg(X, Y)