Comparison among different shrinkage covariance estimators under multicollinearity and high dimensions conditions

Abstract EN

Covariance matrix estimation is a very important process for many multivariate applications like canonical analysis and multivariate hypotheses testing.

Many data conditions require unusual estimation for covariance matrix that be different from the sample covariance matrix because the last (latter) is very weak under conditions like multicollinearity and high dimensions.

Here, we introduce a comparison among three kinds of covariance matrix estimators under multicollinearity and high dimension conditions.

Three estimators were submitted for covariance matrix: the Oracle estimator(OE), Chen estimator CE and sample covariance estimator MLE under Fractional Brownian motion FBM structure covariance matrix to simulate the multicollinearity and the high dimensions conditions.

A comparison was made by using Frobenius distance as a measure of goodness for estimators.

Covariance matrix estimation is a very important process for many multivariate applications like canonical analysis and multivariate hypotheses testing.

Many data conditions require unusual estimation for covariance matrix that be different from the sample covariance matrix because the last (latter) is very weak under conditions like multicollinearity and high dimensions.

Here, we introduce a comparison among three kinds of covariance matrix estimators under multicollinearity and high dimension conditions.

Three estimators were submitted for covariance matrix: the Oracle estimator(OE), Chen estimator CE and sample covariance estimator MLE under Fractional Brownian motion FBM structure covariance matrix to simulate the multicollinearity and the high dimensions conditions.

A comparison was made by using Frobenius distance as a measure of goodness for estimators.