Estimation of Shift and Center of Symmetry Based on Kolmogorov-Smirnov Statistics

A point estimator and a set of confidence intervals based on the Kolmogorov-Smirnov statistic are proposed for the shift parameter in the two-sample problem. Asymptotic distibution of the etimator as well as asymptotic bounds for the lengths of the intervals are derived. The two-sample results are then adapted to the one-sample problem to define an estimator and a set of confidence intervals for the center of a symmetric population.