Dependent Bootstrap Confidence Intervals for a Population Mean

Abstract

This study compares and analyzes the coverage probabilities and the average interval lengths of confidence interval for a population mean based on the dependent bootstrap procedure against those based on the independent bootstrap procedure.  Both dependent and independent bootstrap confidence intervals for a population mean are computed by the Bootstrap-t, Percentile, and Modified Percentile methods.  Simulations show that the coverage probabilities of the dependent bootstrap confidence intervals are similar to those of the independent bootstrap confidence intervals.  The average interval lengths of the dependent bootstrap method are shorter for most situations.  For both the independent and dependent bootstrap confidence intervals, the coverage probabilities increase and the average interval lengths decrease as the sample size n increase for Normal, Gamma, and Chi-square distributions, as well as three methods used in this work.