Abstract
This paper gives three easily computed highly outlier resistant robust $\sqrt{n}$ consistent estimators of multivariate location and dispersion for elliptically contoured distributions with fourth moments. When the data is from a multivariate normal distribution, the dispersion estimators are also consistent estimators of the covariance matrix. Outlier detection and robust canonical correlation analysis are presented as applications.
Highlights
This paper gives three robust estimators of multivariate location and dispersion and uses one of the estimators to create a robust method of canonical correlation analysis
When the data is from a multivariate normal distribution, the dispersion estimators are consistent estimators of the covariance matrix
The reweighted FCH (RFCH) estimator is the second estimator while the RMVN estimator is so named because it is a reweighted FCH estimator that can give useful estimates of the population covariance matrix when the data is from a multivariate normal distribution, even when certain types of outliers are present
Summary
This paper gives three robust estimators of multivariate location and dispersion and uses one of the estimators to create a robust method of canonical correlation analysis. The reweighted FCH (RFCH) estimator is the second estimator while the RMVN estimator is so named because it is a reweighted FCH estimator that can give useful estimates of the population covariance matrix when the data is from a multivariate normal distribution, even when certain types of outliers are present.
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