Optimal estimators for threshold-based quality measures

We consider a problem in parametric estimation: given n samples from an unknown distribution,we want to estimate which distribution,from a given one-parameter family,produced the data. following schulman and vazirani (2005),we evaluate an estimator in terms of the chance of being within a specified tolerance of the correct answer,in the worst case. we provide optimal estimators for several families of distributions on . we prove that for distributions on a compact space,there is always an optimal estimator that is translation invariant,and we conjecture that this conclusion also holds for any distribution on . by contrast,we give an example showing that,it does not hold for a certain distribution on an infinite tree. copyright © 2010 aaron abrams et al.