cov.wcomed: Weighted Co-Median Robust Covariance Matrix

In abnormally-distributed/cvreg: Cross Validation and Robust Estimation Utilities

Description

See cov.comed for details on how the co-median matrix is calculated. The difference in this function is that the final covariance matrix is not based on dropping identified outliers, but rather, smoothly downweighting them.

Usage

cov.wcomed(x, hd = F, method = c("med", "hd", "aad"), iter = 2, k = 1.5)

Arguments

x	a data frame or matrix containing numeric variables
method	one of "med", "hd", or "aad". "med" uses the typical median and MAD. "hd" uses the Harrell-Davis estimate of the median in place of the median, and "aad" uses the average absolute deviation in lieu of the median absolute deviation. if option "aad" is used the appropriate consistency constant, sqrt(pi/2), is used instead of 1.4826. the only time "aad" is preferable is when there are columns in the data with a median absolute deviation of zero.
iter	number of refinement iterations

Value

a covRobust object containing the following elements:

• center: multivariate mean of cleaned data set after discarding outliers identified by the mahalanobis distances of the co-median matrix.

• cov: covariance matrix of cleaned data set after discarding outliers identified by the mahalanobis distances of the co-median matrix.

• medians: estimated columnwise medians

• com: estimated co-median matrix

• delta: the initial raw comedian correlation matrix

• dist: the mahalanobis distances based on the cleaned covariance matrix

• distL1: the mahalanobis distances based on the co-median matrix

• outliers: the indices of the outliers identified by the co-median matrix based mahalanobis distances; these are the points removed to obtain the cleaned covariance matrix.

• weights: the weights for downweighting outliers.

References

Falk, M. (1997) On MAD and comedians. Annals of the Institute of Statistical Mathematics 49, 615-644.

Falk, M. (1998). A Note on the Comedian for Elliptical Distributions. Journal of Multivariate Analysis, 67(2), 306-317. doi:10.1006/jmva.1998.1775

Harrell, F. E. & Davis, C. E. (1982). A new distribution-free quantile estimator. Biometrika, 69, 635–640

Sajesh, T. A., & Srinivasan, M. R. (2012). Outlier detection for high dimensional data using the Comedian approach. Journal of Statistical Computation and Simulation, 82(5), 745-757. doi:10.1080/00949655.2011.552504

Examples

cov.wcomed(x)

abnormally-distributed/cvreg documentation built on May 3, 2020, 3:45 p.m.