huber.cov {FarmTest}

Tuning-free Huber-type covariance estimation

Description

The function calculates adaptive Huber-type covariance estimator from a data sample, with robustification parameter \tau determined by a tuning-free principle. For the input matrix X, both low-dimension (p < n) and high-dimension (p > n) are allowed.

Usage

huber.cov(X)

Arguments

X

An n by p data matrix.

Value

A p by p Huber-type covariance matrix estimator will be returned.

References

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

Ke, Y., Minsker, S., Ren, Z., Sun, Q. and Zhou, W.-X. (2019). User-friendly covariance estimation for heavy-tailed distributions. Statis. Sci., 34, 454-471.

See Also

huber.mean for tuning-free Huber mean estimation and huber.reg for tuning-free Huber regression.

Examples

n = 100
d = 50
X = matrix(rt(n * d, df = 3), n, d) / sqrt(3)
Sigma = huber.cov(X)