A robust paired t-test is a better choice for skewed distributions than the conventional paired t-test (e.g Fradrette, Keselman, Lix, & Wilcox, 2003). One version of the robust test uses a trimmed mean and a Winsorized variance. Is there a way to find the optimal cutoff point for the Winsorization percentiles that maximises the sensitivity?
If I understand correctly, robust statistics perform better for skewed distributions than for symmetric ones and modifying the tails of the distributions using Winsorization or trimming thus changes the skewness. For example, consider if one were to increase the Winsorization percentage iteratively. I imagine that the skewness statistic approaches a certain criterion and the adjusted $R^2$ difference for the cross-correlation between the original distribution and the current Winsorized distribution approaches a criterion close to zero.
If using such an algorithm, would it be possible to reach an unbiased estimates of central tendency and measures of dispersion? Are there any known implementations, for example, in the field of machine learning?
Fradrette, K., Keselman, H. J., Lix, L., Algina, J., & Wilcox, R. R. (2003). Conventional and robust paired independent-samples t test: Type I error and power rate. Journal of Modern Applied Statistical Methods, 2(2) 22, 480-496. Retrieved from http://digitalcommons.wayne.edu/jmasm/vol2/iss2/22 [Open Access] 2016-08-25.