FarmTest (version 2.0.1)

farm.cov: 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

farm.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<U+2013>101.

Ke, Y., Minsker, S., Ren, Z., Sun, Q. and Zhou, W.-X. (2019). User-friendly covariance estimation for heavy-tailed distributions: A survey and recent results. Statis. Sci., to appear.

See Also

farm.mean for tuning-free Huber mean estimation.

Examples

# NOT RUN {
set.seed(2019)
n = 100
d = 50
X = matrix(rt(n * d, df = 3), n, d) / sqrt(3)
Sigma = farm.cov(X)
# }