Split sample skewness

Iftikhar Hussain Adil, Abdul Wahid and Edmund H. Mantell

Communications in Statistics - Theory and Methods, 2021, vol. 50, issue 22, 5171-5188

Abstract: The shape of a statistical distribution of data is important in such diverse areas as descriptive analysis, risk analysis, portfolio optimization and strategic decision making. If it is known (or believed) that the probability density function of a random variable is not symmetric, the question of its skewness becomes important. Various methods of assessing skewness have been formulated, but none are totally satisfactory. The classical measurement of skewness is based on higher moments of the random variable about its mean. However, it is well known that those measurements are sensitive to extreme outliers. The implication of the sensitivity is that mean-based metrics of skewness are inefficient, especially in small or medium size sample data. Those mean-based metrics are known as Pearson skewness, Quartile skewness and Octile skewness. All have been devised to try to accommodate for the presence of outliers. However, those test statistics are demonstrably inefficient in the presence of outliers. That inefficiency motivates the approach in this paper; the development of an efficient and more robust skewness metric we call Split Sample Skewness, hereafter referred to as SSS. In this context, efficiency means that the SSS metric requires fewer sample observations than the less efficient metrics cited above to achieve the same level of statistical robustness. The name reflects a methodology that partitions the sample into two subgroups at the median. This paper displays the findings of multiple simulation studies adducing evidence bearing on the efficiency of split ample skewness relative to other measures of skewness.

Date: 2021
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DOI: 10.1080/03610926.2020.1804588

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