Question

Econometrics:

Explain statistical robustness tests for estimated coefficients and overall equation.

Answer 1

Ans- In statistics, the term robust or robustness refers to the power/strength of a statistical model, tests, and procedures according to the specific conditions of the statistical analysis a study hopes to achieve. Given that these conditions of a study are met, the models can be verified to be true through the use of mathematical proofs.

Robust statistics are statistics with good performance for data drawn from a wide range of probability distributions, especially for distribution that is not normal. Robust statistical methods have been developed for many common problems, such as estimating the location, scale, and regression parameters.  

Robustness tests emerged as social scientists’ response to the uncertainty they face in specifying empirical models. The dominant conception of robustness, which judge whether the estimated effects remain statistically significant in all robustness test models, results in flawed inferential logic. Even if the baseline estimation model were correctly specified, null hypothesis significance testing is problematic. It loses its inferential value when multiple models are estimated to explore the stability of the baseline model’s estimated effect to plausible alternative specification choices.

The practice of robustness testing put an end to the idea that a single model, a single parameter estimate and its sampling error can be used to make valid statistical inferences. But it depends on the users of data on how they interpreted this and use it in there use.

In most cases, robustness has been established through technical work in mathematical statistics, and, fortunately, we do not necessarily need to do these advanced mathematical calculations in order to properly utilize them, We only need to understand what the overall guidelines are for robustness of our specific statistical method.T-procedures function as robust statistics because they typically yield good performance per these models by factoring in the size of the sample into the basis for applying the procedure.