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Cao, Jennifer Yue 2012-11-05T16:15:33Z 2012-11-05T16:15:33Z 2012-11-05 2012 December http://hdl.handle.net/2097/14897 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. Master of Science Masters Department of Statistics Paul I. Nelson en_US Kansas State University © the author. This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). http://rightsstatements.org/vocab/InC/1.0/ Confidence Interval Median Cauchy Trimmed Mean Statistics (0463) The performance and robustness of confidence intervals for the median of a symmetric distribution constructed assuming sampling from a Cauchy distribution Report open.access