On a Theoretical Background for Computing Reliable Approximations of the Barankin Bound

SANTIAGO GONZALEZ ZERBO; BRUNO CERNUSCHI FRÍAS

Rosario, Santa Fe

Congreso; 13º Simposio Argentino de Investigación Operativa, 44JAIIO Jornadas Argentinas de Informática, 2015.; 2015

SADIO, Sociedad Argentina de Informática

The Barankin bound is locally the greatest possible lowerbound for the variance of any unbiased estimator of a deterministic parameter, under certain relatively mild conditions. Much more essential,Barankin´s work determines the sufficient and necessary conditions under which an unbiased estimator with finite variance exists. Nevertheless,the computing of this bound, along with the proof of existence or non-existence of the estimator, has shown to be extremely challenging in mostcases. Thereby, many approaches have been made to attain easily computable approximations of the bound, given it exists. Focusing on therather central matter of existence, we provide a simple theoretical framewithin which our approximations of the bound give a clear insight onwhether an unbiased estimator does exist.