Construction of Fiducial Confidence Intervals for the Mixture of Cauchy and Normal Distributions
Yuriy Glagovskiy
Master's Candidate
Department of Statistics
Colorado State University
 
Thursday, July 6, 2006
10:00 a.m.
006 Statistics Building

ABSTRACT

Fiducial Inference was first introduced by Fisher as an alternative to Bayesian Inference for such problems, where little information was available about the domain of model parameters. However, Fiducial Inference was not popular among statisticians due to a controversy associated with Fisher's approach. Nowadays with emergence of powerful computers statisticians return to Fisher's ideas by considering Fiducial argument as a generic tool for receiving approximate confidence intervals by simulations.

In this talk performance of Fiducial Inference in application to construction of simultaneous confidence intervals for the parameters of mixture of Cauchy and Normal distributions is discussed. Small scale simulation study was carried out to evaluate reliability of confidence intervals for mixture parameters. It was shown that the confidence intervals received for the mean of Normal distribution and the binomial parameter p are reliable. The result of this work might be useful in Robust Statistics to make inference in case of the Normal data mixed with outliers.

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