Advances and Applications in Statistics
Volume 52, Issue 2, Pages 121 - 144
(February 2018) http://dx.doi.org/10.17654/AS052020121 |
|
TRANSFORMATIONS, MEANS, AND ACCURATE CONFIDENCE INTERVALS
M. Rekkas and O. Wong
|
Abstract: In this paper, we consider the problem of constructing confidence intervals for the mean of a positively skewed distribution. Theoretically, if the sample size is large enough, the central limit theorem and the bootstrap method can be applied regardless of the population distribution. However, when the sample size is small and the population distribution is positively skewed, practitioners tend to apply the back transformation method or the generalized p-value method, if available. We propose a highly accurate alternative to obtaining a confidence interval for this mean which is ground in higher-order asymptotic likelihood theory. We compare our approach to some commonly used approaches in the literature. We show the superiority of our proposed method using simulation analyses. Our approach is both easy to implement and provides superior coverage in small samples. |
Keywords and phrases: confidence intervals, p-values, likelihood analysis, transformations. |
|
Number of Downloads: 447 | Number of Views: 3404 |
|