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Inference about the Population Kurtosis with Confidence: Parametric and Bootstrap Approaches

This paper considers some classical and bootstrap methods in constructing confidence intervals for the kurtosis parameter of a distribution. The bootstrap techniques used are: Bias-Corrected Standard Bootstrap, Efron’s Percentile Bootstrap, Hall’s Percentile Bootstrap and Bias-Corrected Percentile Bootstrap. The performance of these estimators is compared through confidence intervals by determining the average width and probabilities of capturing the kurtosis parameter of a distribution. We observed that the parametric method works well in terms of coverage probability when data come from a normal distribution, while the bootstrap intervals struggled in constantly reaching a 95% confidence level. When sample data are from a distribution with negative kurtosis, both parametric and bootstrap confidence intervals performed well, although we noticed that bootstrap methods tend to have shorter intervals. When it comes to positive kurtosis, bootstrap methods perform slightly better than classical methods in the sense of high coverage probability. For illustration purposes, two real life health related data are analyzed.