The performance and robustness of confidence intervals for the median of a symmetric distribution constructed assuming sampling from a Cauchy distribution

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dc.contributor.author Cao, Jennifer Yue
dc.date.accessioned 2012-11-05T16:15:33Z
dc.date.available 2012-11-05T16:15:33Z
dc.date.issued 2012-11-05
dc.identifier.uri http://hdl.handle.net/2097/14897
dc.description.abstract Trimmed means are robust estimators of location for distributions having heavy tails. Theory and simulation indicate that little efficiency is lost under normality when using appropriately trimmed means and that their use with data from distributions with heavy tails can result in improved performance. This report uses the principle of equivariance applied to trimmed means sampled from a Cauchy distribution to form a discrepancy function of the data and parameters whose distribution is free of the unknown median and scale parameter. Quantiles of this discrepancy function are estimated via asymptotic normality and simulation and used to construct confidence intervals for the median of a Cauchy distribution. A nonparametric approach based on the distribution of order statistics is also used to construct confidence intervals. The performance of these intervals in terms of coverage rate and average length is investigated via simulation when the data are actually sampled from a Cauchy distribution and when sampling is from normal and logistic distributions. The intervals based on simulation estimation of the quantiles of the discrepancy function are shown to perform well across a range of sample sizes and trimming proportions when the data are actually sampled from a Cauchy distribution and to be relatively robust when sampling is from the normal and logistic distributions. en_US
dc.language.iso en_US en_US
dc.publisher Kansas State University en
dc.subject Confidence Interval Median en_US
dc.subject Cauchy Trimmed Mean en_US
dc.title The performance and robustness of confidence intervals for the median of a symmetric distribution constructed assuming sampling from a Cauchy distribution en_US
dc.type Report en_US
dc.description.degree Master of Science en_US
dc.description.level Masters en_US
dc.description.department Department of Statistics en_US
dc.description.advisor Paul Nelson en_US
dc.subject.umi Statistics (0463) en_US
dc.date.published 2012 en_US
dc.date.graduationmonth December en_US

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