Robustness of three power transformation estimation procedures

Abstract

Maximum likelihood, goodness-of-fit, and symmetric percentile estimators of the power transformation parameterp, are considered. The comparative robustness of each estimation procedure is evaluated when the transformed data can be made symmetric, but may not necessarily be normal. Seven types of symmetric distributions are considered as well as four contaminated normal distributions over a range of six p values for samples of size 25, 50, and 100. The results indicate that the maximum likelihood estimator was slightly better than the goodness-of-fit estimator, but both were greatly superior to the percentile estimator. In general, the procedures were robust to distributional symmetric departures from normality, but increasing kurtosis caused appreciable increases in variation for estimated p values. The variability of p was found to decrease more than exponentially with decreases in the underlying normal distribution coefficient of variation. The standard likelihood ratio confidence interval procedure was...