What are the limitations of maximum likelihood estimation procedures when a majority of the observations are below the limit of detection?

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Roberto Molteni

It is suggested Maximum Likelihood Estimation (MLE) approach when the proportion of Non Detected (ND) is less than 50 percent and if the data without the ND values are normally distributed.

(U.S. Environmental Protection Agency (2006a) Data Quality Assessment: Statistical Methods for Practitioners. EPA/240-B-06/003. February 2006).

Whatever approach you will use, it is recommended to record all assumptions (especially distribution assumptions).