The wide-sense parametric coverage estimator against the distribution mismatch problem for sparse data

Abstract

Robust parameter estimation of sparse data is generally applied to the tasks when data collection is time-consuming or of high cost. We point out a new problem caused by sparse data. We find that there may exists coverage mismatch between data samples and the population when the sample size is less than 20. We call it the distribution mismatch (DM) problem. In this study, we derive a wide-sense joint pdf for coverage, range, the sample of minimum order, and data samples themselves to analyze the DM problem. Based on the formulation, a new algorithm is proposed to compensate the DM problem. Experimental results show that the mean estimate of the algorithm will converge to the population mean if the standard deviation of population is known.