adaHuber.cov {adaHuber} | R Documentation |
Adaptive Huber Covariance Estimation
Description
Adaptive Huber covariance estimator from a data sample, with robustification parameter \tau
determined by a tuning-free principle.
Usage
adaHuber.cov(X, epsilon = 1e-04, iteMax = 500)
Arguments
X |
An |
epsilon |
(optional) The tolerance level in the iterative estimation procedure. The problem is converted to mean estimation, and the stopping rule is the same as |
iteMax |
(optional) Maximum number of iterations. Default is 500. |
Details
The observed data X
is an n
by p
matrix. The distribution of each entry can be asymmetrix and/or heavy-tailed. The function outputs a robust estimator for the covariance matrix of X
. For the input matrix X
, both low-dimension (p < n
) and high-dimension (p > n
) are allowed.
Value
A list including the following terms will be returned:
means
The Huber estimators for column means. A
p
-dimensional vector.cov
The Huber estimator for covariance matrix. A
p
byp
matrix.
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
adaHuber.mean
for adaptive Huber mean estimation.
Examples
n = 100
p = 5
X = matrix(rt(n * p, 3), n, p)
fit.cov = adaHuber.cov(X)
fit.cov$means
fit.cov$cov