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OPTIMAL ESTIMATORS FOR THRESHOLD-BASED QUALITY MEASURES
 

Summary: OPTIMAL ESTIMATORS FOR THRESHOLD-BASED
QUALITY MEASURES
AARON ABRAMS, SANDY GANZELL, HENRY LANDAU, ZEPH LANDAU, JAMES
POMMERSHEIM, AND ERIC ZASLOW
Abstract. We consider a problem in parametric estimation: given n
samples from an unknown distribution, we want to estimate which dis-
tribution, from a given one-parameter family, produced the data. Fol-
lowing Schulman and Vazirani [12], 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 R. 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 R.
By contrast, we give an example showing it does not hold for a certain
distribution on an infinite tree.
1. Introduction
Estimating probability distribution functions is a central problem in sta-
tistics. Specifically, beginning with an unknown probability distribution on
an underlying space X, one wants to be able to do two things: first, given
some empirical data sampled from the unknown probability distribution,

  

Source: Abrams, Aaron - Department of Mathematics and Computer Science, Emory University

 

Collections: Mathematics