Robust confidence intervals for the difference of two independent population variances

Abstract

In this study, we propose confidence intervals and their bootstrap ver sions for the difference of variances of two independent population using robust variance estimators which are binary distance squared, binary distance median squared, and comedian. The proposed confidence in tervals are compared with Herbert confidence interval in terms of cov erage probability and average width for normal and some skewed distri butions. A simulation study is conducted to evaluate performances of the proposed confidence intervals under different scenarios. The sim ulation results indicate that coverage probabilities for the proposed confidence intervals are very close to nominal confidence levels when population variances difference is equal to zero. Confidence interval based on binary distance produces the narrowest average widths. Her bert confidence interval have not perform well for skewed distribution populations. Confidence interval based on comedian is generally rec ommended when difference between non-normal population variance not equal to zero. Average widths of bootstrap percentile confidence intervals are smaller, and decreases as sample size and nominal size increases, as expected. Consequently, we recommend bootstrap per centile confidence intervals based on binary distances for non-normal distributions.