Robust Estimation in Non-normal Samples with Known Detection Limits

Abstract

Non-detected values, which are the observations below or above a limit of detection, are almost inevitable in most environmental data sets and in HIV studies. The common approach is replacing the non-detected observations with the LOD values, log-transforming the data and using standard procedures to estimate the parameters of a normally distributed population. In this study, we discuss the case when the data is not necessarily from a lognormal population, which is a more realistic situation from a practical point of view. We derive the modified maximum likelihood estimators of the mean and the standard deviation,and develop procedures for hypothesis testing of the population mean under non-normality. We show that the derived MMLEs are much more precise than those obtained by using the traditional approach. We study the robustness properties of the proposed estimators under plausible deviations from an assumed model, and show that derived estimators are highly robust with respect to data anomalies. We apply the method to the NHANES data.