Robust confidence intervals for the difference of two independent population variances


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AKYÜZ H. E. , GAMGAM H.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, cilt.49, sa.1, ss.478-493, 2020 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 49 Konu: 1
  • Basım Tarihi: 2020
  • Doi Numarası: 10.15672/hujms.475318
  • Dergi Adı: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Sayfa Sayıları: ss.478-493

Özet

In this study, we propose confidence intervals and their bootstrap versions for the difference of variances of two independent population using some robust variance estimators. The proposed confidence intervals are compared with Herbert confidence interval in terms of coverage probability and average width. A simulation study is conducted to evaluate performances of the proposed confidence intervals under different scenarios. The simulation results indicate that the coverage probabilities for the proposed confidence intervals are very close to nominal confidence levels when the difference of population variances is zero. Confidence interval based on binary distance produces the narrowest average widths. Herbert confidence interval have not perform well for skewed distribution populations. Confidence interval based on comedian is generally recommended when the difference of population variances for skewed distributions is not 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 percentile confidence interval based on binary distances for skewed distributions.