Thanks to lots of helpful answers in the community, I figured that Least Absolute Deviations regression can give better estimations when the normality of residuals is violated (e.g. residuals following Laplace distribution).
Meanwhile, a thought also came to my mind that in general with large sample size the parametric assumption of residuals following normal distribution need not have to be fulfilled, due to the central limit theorem. Then, considering that research nowadays often manage a great amount of data, is it valid to assume that there are few cases where researcher have to use LAD due to the issue of normality?
- In a similar vein, if sample size provides a good buffer to the problem of normality of error, then it perhaps seems techniques such as log-transformation of skewed variables won't be needed much also.