Robust confidence intervals for the difference oftwo independent population variances

Abstract

In this study, we propose confidence intervals and their bootstrap versions for the differ-ence of variances of two independent population using some robust variance estimators.The proposed confidence intervals are compared with Herbert confidence interval in termsof coverage probability and average width. A simulation study is conducted to evaluateperformances of the proposed confidence intervals under different scenarios. The simula-tion results indicate that the coverage probabilities for the proposed confidence intervalsare very close to nominal confidence levels when the difference of population variancesis zero. Confidence interval based on binary distance produces the narrowest averagewidths. Herbert confidence interval have not perform well for skewed distribution pop-ulations. Confidence interval based on comedian is generally recommended when thedifference of population variances for skewed distributions is not zero. Average widthsof bootstrap percentile confidence intervals are smaller, and decreases as sample size andnominal size increases, as expected. Consequently, we recommend bootstrap percentileconfidence interval based on binary distances for skewed distributions.