I published a new paper with my coauthors Jessica Meyer, András Bárdossy, and Beth Parker entitled "Estimating a Representative Value and Proportion of True Zeros for Censored Analytical Data with Applications to Contaminated Site Assessment" in Environmental Science & Technology (with Suplemental Information).
With Jessi I had had the idea that this might work quite some time ago, but it took some time to get the analysis done and to get it in a concise form. I am pretty happy with the outcome. The statistical model is parsimoneous and leads to nice results at a real field site.
The following figure shows that the likelihood function has a better optimum when the proportion of true zeros is estimated in addition to the typical parameters of a distribution function (up to a fairly large portion of censored values):
To my knowledge this is one of only few studies based on real data that incorporate censored measurements in a meaningful way. In our application we estimated the mass of a solute at certain locations in a given geological section. Hence this result has important implications for remedial design. Even more, we think this has direct implications for any variable that is measured in nature.
Due to the strict space-limitations for an ES&T paper, there are some really nice figures left out in the paper, which are plotted in the suplemental information, e.g.,
- regarding a verification of the frequency of true zeros in the case of a precipitation data-set;
- an analysis of the proportion of true zeros of a regional groundwater quality data-set (contaminants with a relatively short time in the environment exhibit fairly large portions of true zeros);
- information regarding the robustness, stability, and unbiasedness of the method;