Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2020, Cilt: 49 Sayı: 1, 478 - 493, 06.02.2020
https://doi.org/10.15672/hujms.475318

Öz

Kaynakça

  • [1] M.O.A. Abu-Shawiesh, S. Banik and , B.M.G. Kibria, A simulation study on some confidence intervals for the population standard deviation, SORT-Stat. Oper. Res. Trans. 35 (2), 83-102, 2011.
  • [2] H.E. Akyüz, Interval estimation based on robust estimators for the difference of two independent population variances, Gazi University, Graduate School of Natural and Applied Sciences, PhD Thesis, Ankara, Turkey, 2017.
  • [3] H.E. Akyüz, H. Gamgam and A. Yalçınkaya, Interval estimation for the difference of two independent nonnormal population variances, Gazi University Journal of Science 30 (3),117-129, 2017.
  • [4] H.E. Akyüz and H. Gamgam, Interval estimation for nonnormal population variance with kurtosis coefficient based on trimmed mean, Turkiye Klinikleri Journal of Biostatistics 9 (3), 213-221, 2017.
  • [5] H.E. Akyüz and H. Gamgam, Comparison of binary logistic regression models based on bootstrap method: an application on coronary artery disease data, Gazi University Journal of Science 32 (1), 318-331, 2019.
  • [6] C. Atakan, Bootstrap percentile confidence intervals for actual error rate in linear discriminant analysis, Hacet. J. Math. Stat. 38 (3), 357-372, 2009.
  • [7] A.M. Barham and S. Jeyaratnam Robust confidence interval for the variance, J. Stat. Comput. Simul. 62 (3), 189-205, 1999.
  • [8] D.G. Bonett, Approximate confidence interval for standard deviation of nonnormal distributions, Comput. Statist. Data Anal. 50 (3), 775-782, 2006.
  • [9] B.D. Burch, Nonparametric bootstrap confidence intervals for variance components applied to interlaboratory comparisons, J. Agric. Biol. Environ. Stat. 17 (2), 228-245, 2012.
  • [10] B.D. Burch, Estimating kurtosis and confidence ntervals for the variance under nonnormality, J. Stat. Comput. Simul. 84 (12), 2710-2720, 2014.
  • [11] B.D. Burch, Distribution-dependent and distribution-free confidence intervals for the variance, Stat. Methods Appl. 26 (4), 629-648, 2017.
  • [12] J. Carpenter and J. Bithell, Bootstrap confidence intervals: when, which, what? A practical guide for medical statisticians, Stat. Med. 19 (9), 1141-1164, 2000.
  • [13] G. Casella and R.L. Berger Statistical Inference, Duxbury Thomson Learning, USA, 2002.
  • [14] V. Cojbasica and A. Tomovica, Nonparametric confidence intervals for population variance of one sample and the difference of variances of two samples, Comput. Statist. Data Anal. 51 (12), 5562-5578, 2007.
  • [15] V. Cojbasica and V. Loncar, One-sided confidence intervals for population variances of skewed distributions, J. Statist. Plann. Inference 141 (5), 1667-1672, 2011.
  • [16] C. Croux and P.J. Rousseeuw, A class of high-breakdown scale estimators based on subranges, Comm. Statist. Theory Methods 21 (7), 1935-1951, 1992.
  • [17] B. Efron, Bootstrap methods: Another look at the jackknife, Ann. Statist. 7 (1), 1-26, 1979.
  • [18] B. Efron and R.J. Tibshirani, An Introduction to the Bootstrap, Chapman & Hall/CRC, USA, 1993.
  • [19] M. Falk, Asymptotic independence of median and MAD, Statist. Probab. Lett. 34 (4), 341-345, 1997.
  • [20] R.D. Herbert, A. Hayen, P. Macaskill and S.D. Walter, Interval estimation for the difference of two independent variances, Comm. Statist. Simulation Comput. 40 (5), 744-758, 2011.
  • [21] S. Niwitpong, Confidence intervals for the difference of two normal population variances, World Academy of Science, Engineering and Technology 5 (8), 602-605, 2011.
  • [22] S. Niwitpong, A note on coverage probability of confidence interval for the difference between two normal variances, Appl. Math. Sci. 6 (67), 3313-3320, 2012.
  • [23] M.J. Panik, Advanced Statistics from an Elementary Point of View, 1st edition, USA: Academic Press, Elsevier, 2005.
  • [24] I.M. Paul, J. Beiler, A. McMonagle, M.L. Shaffer, L. Duda and C.M. Berlin, Effect of honey, dextromethorphan, and no treatment on nocturnal cough and sleep quality for coughing children and their parents, Archives of Pediatrics and Adolescent Medicine 161 (12), 1140-1146, 2007.
  • [25] P.J. Rousseeuw and C. Croux, Alternatives to the median absolute deviation, J. Amer. Statist. Assoc. 88 (424), 1273-1283, 1993.
  • [26] H. Scheffe, The Analysis of Variance, Wiley, New York, 1959.
  • [27] S. Suwan and S. Niwitpong, Interval estimation for a linear function of variances of nonnormal distributions that utilize the kurtosis, Appl. Math. Sci. 7 (99), 4909-4918, 2013.
  • [28] W. Thangjai and S. Niwitpong, Simultaneous Confidence Intervals for All Differences of Variances of Log-Normal Distributions, In International Conference of the Thailand Econometrics Society (pp. 235-244). Springer, Cham.,2019.
  • [29] V. Zardasht, A bootstrap test for symmetry based on quantiles, Hacet. J. Math. Stat., 47 (4), 1061-1069, 2018.

Robust confidence intervals for the difference of two independent population variances

Yıl 2020, Cilt: 49 Sayı: 1, 478 - 493, 06.02.2020
https://doi.org/10.15672/hujms.475318

Öz

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.

Kaynakça

  • [1] M.O.A. Abu-Shawiesh, S. Banik and , B.M.G. Kibria, A simulation study on some confidence intervals for the population standard deviation, SORT-Stat. Oper. Res. Trans. 35 (2), 83-102, 2011.
  • [2] H.E. Akyüz, Interval estimation based on robust estimators for the difference of two independent population variances, Gazi University, Graduate School of Natural and Applied Sciences, PhD Thesis, Ankara, Turkey, 2017.
  • [3] H.E. Akyüz, H. Gamgam and A. Yalçınkaya, Interval estimation for the difference of two independent nonnormal population variances, Gazi University Journal of Science 30 (3),117-129, 2017.
  • [4] H.E. Akyüz and H. Gamgam, Interval estimation for nonnormal population variance with kurtosis coefficient based on trimmed mean, Turkiye Klinikleri Journal of Biostatistics 9 (3), 213-221, 2017.
  • [5] H.E. Akyüz and H. Gamgam, Comparison of binary logistic regression models based on bootstrap method: an application on coronary artery disease data, Gazi University Journal of Science 32 (1), 318-331, 2019.
  • [6] C. Atakan, Bootstrap percentile confidence intervals for actual error rate in linear discriminant analysis, Hacet. J. Math. Stat. 38 (3), 357-372, 2009.
  • [7] A.M. Barham and S. Jeyaratnam Robust confidence interval for the variance, J. Stat. Comput. Simul. 62 (3), 189-205, 1999.
  • [8] D.G. Bonett, Approximate confidence interval for standard deviation of nonnormal distributions, Comput. Statist. Data Anal. 50 (3), 775-782, 2006.
  • [9] B.D. Burch, Nonparametric bootstrap confidence intervals for variance components applied to interlaboratory comparisons, J. Agric. Biol. Environ. Stat. 17 (2), 228-245, 2012.
  • [10] B.D. Burch, Estimating kurtosis and confidence ntervals for the variance under nonnormality, J. Stat. Comput. Simul. 84 (12), 2710-2720, 2014.
  • [11] B.D. Burch, Distribution-dependent and distribution-free confidence intervals for the variance, Stat. Methods Appl. 26 (4), 629-648, 2017.
  • [12] J. Carpenter and J. Bithell, Bootstrap confidence intervals: when, which, what? A practical guide for medical statisticians, Stat. Med. 19 (9), 1141-1164, 2000.
  • [13] G. Casella and R.L. Berger Statistical Inference, Duxbury Thomson Learning, USA, 2002.
  • [14] V. Cojbasica and A. Tomovica, Nonparametric confidence intervals for population variance of one sample and the difference of variances of two samples, Comput. Statist. Data Anal. 51 (12), 5562-5578, 2007.
  • [15] V. Cojbasica and V. Loncar, One-sided confidence intervals for population variances of skewed distributions, J. Statist. Plann. Inference 141 (5), 1667-1672, 2011.
  • [16] C. Croux and P.J. Rousseeuw, A class of high-breakdown scale estimators based on subranges, Comm. Statist. Theory Methods 21 (7), 1935-1951, 1992.
  • [17] B. Efron, Bootstrap methods: Another look at the jackknife, Ann. Statist. 7 (1), 1-26, 1979.
  • [18] B. Efron and R.J. Tibshirani, An Introduction to the Bootstrap, Chapman & Hall/CRC, USA, 1993.
  • [19] M. Falk, Asymptotic independence of median and MAD, Statist. Probab. Lett. 34 (4), 341-345, 1997.
  • [20] R.D. Herbert, A. Hayen, P. Macaskill and S.D. Walter, Interval estimation for the difference of two independent variances, Comm. Statist. Simulation Comput. 40 (5), 744-758, 2011.
  • [21] S. Niwitpong, Confidence intervals for the difference of two normal population variances, World Academy of Science, Engineering and Technology 5 (8), 602-605, 2011.
  • [22] S. Niwitpong, A note on coverage probability of confidence interval for the difference between two normal variances, Appl. Math. Sci. 6 (67), 3313-3320, 2012.
  • [23] M.J. Panik, Advanced Statistics from an Elementary Point of View, 1st edition, USA: Academic Press, Elsevier, 2005.
  • [24] I.M. Paul, J. Beiler, A. McMonagle, M.L. Shaffer, L. Duda and C.M. Berlin, Effect of honey, dextromethorphan, and no treatment on nocturnal cough and sleep quality for coughing children and their parents, Archives of Pediatrics and Adolescent Medicine 161 (12), 1140-1146, 2007.
  • [25] P.J. Rousseeuw and C. Croux, Alternatives to the median absolute deviation, J. Amer. Statist. Assoc. 88 (424), 1273-1283, 1993.
  • [26] H. Scheffe, The Analysis of Variance, Wiley, New York, 1959.
  • [27] S. Suwan and S. Niwitpong, Interval estimation for a linear function of variances of nonnormal distributions that utilize the kurtosis, Appl. Math. Sci. 7 (99), 4909-4918, 2013.
  • [28] W. Thangjai and S. Niwitpong, Simultaneous Confidence Intervals for All Differences of Variances of Log-Normal Distributions, In International Conference of the Thailand Econometrics Society (pp. 235-244). Springer, Cham.,2019.
  • [29] V. Zardasht, A bootstrap test for symmetry based on quantiles, Hacet. J. Math. Stat., 47 (4), 1061-1069, 2018.
Toplam 29 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular İstatistik
Bölüm İstatistik
Yazarlar

Hayriye Esra Akyüz 0000-0002-1784-5910

Prof. Dr. Hamza Gamgam 0000-0002-9595-9315

Yayımlanma Tarihi 6 Şubat 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 49 Sayı: 1

Kaynak Göster

APA Akyüz, H. E., & Gamgam, P. D. H. (2020). Robust confidence intervals for the difference of two independent population variances. Hacettepe Journal of Mathematics and Statistics, 49(1), 478-493. https://doi.org/10.15672/hujms.475318
AMA Akyüz HE, Gamgam PDH. Robust confidence intervals for the difference of two independent population variances. Hacettepe Journal of Mathematics and Statistics. Şubat 2020;49(1):478-493. doi:10.15672/hujms.475318
Chicago Akyüz, Hayriye Esra, ve Prof. Dr. Hamza Gamgam. “Robust Confidence Intervals for the Difference of Two Independent Population Variances”. Hacettepe Journal of Mathematics and Statistics 49, sy. 1 (Şubat 2020): 478-93. https://doi.org/10.15672/hujms.475318.
EndNote Akyüz HE, Gamgam PDH (01 Şubat 2020) Robust confidence intervals for the difference of two independent population variances. Hacettepe Journal of Mathematics and Statistics 49 1 478–493.
IEEE H. E. Akyüz ve P. D. H. Gamgam, “Robust confidence intervals for the difference of two independent population variances”, Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 1, ss. 478–493, 2020, doi: 10.15672/hujms.475318.
ISNAD Akyüz, Hayriye Esra - Gamgam, Prof. Dr. Hamza. “Robust Confidence Intervals for the Difference of Two Independent Population Variances”. Hacettepe Journal of Mathematics and Statistics 49/1 (Şubat 2020), 478-493. https://doi.org/10.15672/hujms.475318.
JAMA Akyüz HE, Gamgam PDH. Robust confidence intervals for the difference of two independent population variances. Hacettepe Journal of Mathematics and Statistics. 2020;49:478–493.
MLA Akyüz, Hayriye Esra ve Prof. Dr. Hamza Gamgam. “Robust Confidence Intervals for the Difference of Two Independent Population Variances”. Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 1, 2020, ss. 478-93, doi:10.15672/hujms.475318.
Vancouver Akyüz HE, Gamgam PDH. Robust confidence intervals for the difference of two independent population variances. Hacettepe Journal of Mathematics and Statistics. 2020;49(1):478-93.