Dependent Bootstrap Confidence Intervals for a Population Mean

This study compares and analyzes the coverage probabilities and the averageinterval lengths of confidence interval for a population mean based on the dependentbootstrap procedure against those based on the independent bootstrap procedure. Bothdependent and independent bootstrap confidence intervals for a population mean arecomputed by the Bootstrap-t, Percentile, and Modified Percentile methods. Simulationsshow that the coverage probabilities of the dependent bootstrap confidence intervals aresimilar to those of the independent bootstrap confidence intervals. The average intervallengths of the dependent bootstrap method are shorter for most situations. For both theindependent and dependent bootstrap confidence intervals, the coverage probabilitiesincrease 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.