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What is the concept of robustness in statistics and how is it evaluated?

In statistics, the concept of robustness refers to the ability of a statistical method to provide stable and reliable results even when the underlying assumptions are violated or the data contain outliers. Robust methods are less prone to extreme values ​​or violations of the assumptions and provide robust estimates or test results.

The robustness of a statistical method is usually assessed by comparison with other methods or by simulation experiments. There are several criteria that are taken into account when assessing robustness:

Influence analysis: The method is checked for how strongly individual observations or outliers influence the results. A robust method should be relatively insensitive to single observations that deviate greatly from the rest of the sample.

Comparison with non-robust methods: The robust method is compared with non-robust methods to show that it gives better or comparable results in violation of the assumptions or in the presence of outliers.

Simulation studies: The robustness of a method can be evaluated by simulating data with known properties, such as outliers or violations of assumptions. The results of the method are compared to the true values ​​or the results of other methods to assess their performance.

Theoretical Analysis: In some cases, mathematical or theoretical analysis can be used to assess the robustness of a method. This often involves examining the impact of data breaches on the properties of the method.

It is important to note that robustness is not an absolute property. One method may be more robust than others, but still potentially vulnerable to certain types of breaches or runaways. Therefore, it is advisable to consider different aspects of robustness in order to select the appropriate method for a particular statistical analysis.