Robust Likelihood Ratio Test Based on Gamma Likelihood Function

Abstract

Log transformation was routinely utilized for the analysis of positive continuous random variables. It was usually assumed that the transformed variable has a distribution, more or less, resembling a normal distribution. Further analysis will then be carried out under the assumption of normality. It will be demonstrated that such common practice can lead to seriously biased result, when the distribution that generate the data is not lognormal. An alternative solution will be proposed here. The new method stems from the idea of robust likelihood function introduced by Royall and Tsou (2001). It will be demonstrated that the robustified gamma likelihood function provides unbiased mean parameter estimates, and the corresponding adjusted likelihood ratio test offers correct type I, II error probabilities and correct coverage probabilities, even the true distribution is not gamma.