adaHuber.mean {adaHuber}

Adaptive Huber Mean Estimation

Description

Adaptive Huber mean estimator from a data sample, with robustification parameter \tau determined by a tuning-free principle.

Usage

adaHuber.mean(X, epsilon = 1e-04, iteMax = 500)

Arguments

X

An n-dimensional data vector.

epsilon

(optional) The tolerance level in the iterative estimation procedure, iteration will stop when |\mu_new - \mu_old| < \epsilon. The defalut value is 1e-4.

iteMax

(optional) Maximum number of iterations. Default is 500.

Value

A list including the following terms will be returned:

mu

The Huber mean estimator.

tau

The robustness parameter determined by the tuning-free principle.

iteration

The number of iterations in the estimation procedure.

References

Huber, P. J. (1964). Robust estimation of a location parameter. Ann. Math. Statist., 35, 73–101.

Wang, L., Zheng, C., Zhou, W. and Zhou, W.-X. (2021). A new principle for tuning-free Huber regression. Stat. Sinica, 31, 2153-2177.

Examples

n = 1000
mu = 2
X = rt(n, 2) + mu
fit.mean = adaHuber.mean(X)
fit.mean$mu