Estimating the location parameter under skew normal settings: is violating the independence assumption good or bad?

Researchers typically assume that they are working from a normal distribution and with independent sampling. Both assumptions are often violated. Our goal was to explore the intersection of the violations: Is the net effect good or bad? Using the family of skew-normal distributions, which is a superset of the family of normal distributions, we tested whether the mean squared error (MSE) is less under dependence or under independence. We found that the MSE is less under dependence, under the assumption that elements in both samples are identically distributed related to the population distribution. In addition, increasing skewness and increasing sample size also decrease the MSE. Finally, the largest differences in MSE between dependence and independence occur under moderate skewness.

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