The sample minimum (or maximum) is not an inherently unstable statistic. If there is sufficient density in the distribution near its minimum, the sample minimum

The sample minimum (or maximum) is not an inherently unstable statistic. If there is sufficient density in the distribution near its minimum, the sample minimum can be quite robust. For example, consider that the maximum likelihood estimator for the upper bound of a uniform distribution is simply the sample maximum, and the minimum-variance unbiased estimator is also based on the sample maximum[1]. (This method was used by the Allies in World War 2 to estimate the total number of German tanks by sampling the serial numbers from destroyed tanks[2].) Of course, a real thresholding process would not be perfect, so the lower bound of the distribution of accepted candidates would not be a perfect vertical cutoff as in the examples. Just like any process that adds additional variation to the data, this would reduce the statistical power. You could accept more bias in return for lower variance in your test by taking, say, the 5th percentile instead of the sample minimum as your test statistic. (You can think of the sample minimum as the zeroth percentile.) [1] https://en.wikipedia.org/wiki/Uniform_distribution_%28continuous%29#Estimation_of_maximum https://en.wikipedia.org/wiki/Uniform_distribution_%28contin... [2] https://en.wikipedia.org/wiki/German_tank_problem https://en.wikipedia.org/wiki/German_tank_problem