Robust alternatives to the F-Test in mixed linear models based on MM-estimates

Area of Science:

• Statistics
• Statistical Modeling

Background:

• Mixed linear models are widely used but sensitive to normality assumptions.
• Current robust methods lack direct extensions for likelihood ratio tests.

Purpose of the Study:

• To develop new robust estimators for mixed linear models.
• To enable robust likelihood ratio and Wald-type tests for hypothesis testing.

Main Methods:

• Proposed two novel robust S-estimators for general mixed linear models.
• Investigated theoretical properties and conducted simulation studies.
• Applied the new methods to a real-world dataset.

Main Results:

• The new estimators facilitate robust likelihood ratio and Wald-type tests.
• Simulations and real data analysis demonstrate improved performance with outliers.
• The approach enhances the reliability of hypothesis testing in mixed models.

Conclusions:

• The proposed robust estimators extend robust testing capabilities for mixed linear models.
• This offers a more reliable alternative when normality assumptions are violated.
• The methods are particularly advantageous in the presence of outlying observations.