Robust test statistics for the two-way MANOVA based on the minimum covariance determinant estimator

TL;DR

This paper introduces robust test statistics for two-way MANOVA using the minimum covariance determinant estimator, providing alternatives that are less sensitive to outliers than classical methods.

Contribution

It proposes new robust test statistics based on MCD estimates for two-way MANOVA, improving robustness and efficiency over traditional Wilks' Lambda tests.

Findings

Robust test statistics outperform classical tests in presence of outliers.

Monte Carlo simulations demonstrate improved finite sample accuracy and power.

Application to real data confirms practical effectiveness.

Abstract

Robust test statistics for the two-way MANOVA based on the minimum covariance determinant (MCD) estimator are proposed as alternatives to the classical Wilks' Lambda test statistics which are well known to be very sensitive to outliers as they are based on classical normal theory estimates of generalized variances. The classical Wilks' Lambda statistics are robustified by replacing the classical estimates by highly robust and efficient reweighted MCD estimates. Further, Monte Carlo simulations are used to evaluate the performance of the new test statistics under various designs by investigating their finite sample accuracy, power, and robustness against outliers. Finally, these robust test statistics are applied to a real data example.