farm.cov: Covariance estimation with Huber's loss function

In kbose28/FarmTest: Factor Adjusted Robust Multiple Testing

Description

This function estimates covariance of multivariate data using the Huber's loss. The tuning parameter is chosen by cross validation.

Usage

farm.cov(X, cv = TRUE, tau = 2, verbose = FALSE)

Arguments

X	an n x p data matrix with each row being a sample.
cv	a boolean, specifying whether or not to run cross-validation for the tuning parameter. Default is TRUE.
tau	>0, multiplier for the tuning parameter for Huber loss function. Default is 2. Only used if cv is FALSE. See details.
verbose	a boolean specifying whether to print runtime updates to the console. Default is TRUE.

Details

The tuning parameter = tau * sigma * optimal rate where optimal rate is the optimal rate for the tuning parameter. For details, see Fan et al.(2017). sigma is the standard deviation of the data.

Value

A list with the following items

covhat

the covariance matrix

References

Huber, P.J. (1964). "Robust Estimation of a Location Parameter." The Annals of Mathematical Statistics, 35, 73–101.

Fan, J., Ke, Y., Sun, Q. and Zhou, W-X. (2017). "FARM-Test: Factor-Adjusted Robust Multiple Testing with False Discovery Control", https://arxiv.org/abs/1711.05386.

Zhou, W-X., Bose, K., Fan, J. and Liu, H. (2017). "A New Perspective on Robust M-Estimation: Finite Sample Theory and Applications to Dependence-Adjusted Multiple Testing," Annals of Statistics, to appear, https://arxiv.org/abs/1711.05381.

Examples

set.seed(100)
p = 20
n = 10
X = matrix(rnorm( p*n, 0,1), nrow = n)
covhat = farm.cov(X)

kbose28/FarmTest documentation built on May 29, 2019, 3:01 a.m.