Abstract
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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In probability theory and statistics, the moment generating function of a real-valued random variable (or vector) is an alternative specification of its probability distribution. Thus, it provides the basis of an alternative route to analytical results compared with working directly with probability density functions or cumulative distribution functions.
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Authors would like to thank Dr. Z. Wei (University of Maine) and Dr. R. Steiner (New Mexico State University) for their comments, which lead to the improvement of this paper.
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Communicated by Vladik Kreinovich.
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Wang, C., Wang, T., Trafimow, D. et al. Estimating the location parameter under skew normal settings: is violating the independence assumption good or bad?. Soft Comput 25, 7795–7802 (2021). https://doi.org/10.1007/s00500-021-05679-4
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DOI: https://doi.org/10.1007/s00500-021-05679-4