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Yıl 2023, Cilt: 52 Sayı: 4, 1066 - 1081, 15.08.2023

Samaradasa Weerahandi Malwane Ananda Osman Dağ

https://doi.org/10.15672/hujms.1176840

Öz

Kaynakça

  • [1] M.M.A. Ananda, O. Dag and S. Weerahandi, Heteroscedastic two-way ANOVA under constraints, Commun. Stat. Theory Methods, Doi:10.1080/03610926.2022.2059682, 2022.
  • [2] M.M.A. Ananda and S. Weerahandi, Two-Way ANOVA with unequal cell frequencies and unequal variances, Stat. Sin.7 (3), 631-646, 1997.
  • [3] S.C. Chow and S.G. Wang, Advanced Linear Models, Marcel Dekker, New York, 1994.
  • [4] Y. Fujikoshi, Two-way ANOVA models with unbalanced data, Discrete Math. 116 (1-3), 315-334, 1993.
  • [5] J. Gamage, T. Mathew and S.Weerahandi, Generalized p-values and generalized confidence regions for the multivariate BehrensFisher problem and MANOVA, J. Multivar. Anal. 88 (1), 177189, 2004.
  • [6] R.A. Johnson and S. Weerahandi, A Bayesian solution to the multivariate Behrens- Fisher problem, J Am Stat Assoc 83 (401), 145-149, 1988.
  • [7] R.A. Johnson and D.W. Wichern, Applied Multivariate Statistical Analysis, Prentice Hall Upper Saddle River, NJ, 2002.
  • [8] K. Krishnamoorthy and F. Lu, A parametric bootstrap solution to the MANOVA under heteroscedasticity, J Stat Comput Simul 80 (8), 873887, 2010.
  • [9] K. Krishnamoorthy, F. Lu and T. Mathew, A parametric bootstrap approach for ANOVA with unequal variances: fixed and random models, Comput Stat Data Anal 51 (12), 5731-5742, 2007.
  • [10] X. Li, J. Wang and H. Liang, comparison of several means: a fiducial based approach, Comput Stat Data Anal 55 (5), 1993-2002, 2011.
  • [11] A. Roy and A. Bose, coverage of generalized confidence intervals, J. Multivar. Anal. 100 (7), 1384-1397, 2009.
  • [12] S.M. Sadooghi-Alvandi, A.A. Jafari and H.A. Mardarni-Fard, One-way ANOVA with unequal variances, Commun. Stat. Theory Methods 41 (22), 42004221, 2012.
  • [13] A. Thomson and D. Randall-MacIver, The Ancient Races of the Thebaid: Being an Anthropometrical Study of the Inhabitants of Upper Egypt from the Earliest Prehistoric Times to the Mohammedan Conquest, Based Upon the Examination of Over 1,500 Crania, Clarendon Press, 1905.
  • [14] K. Tsui and S. Weerahandi, Generalized p-values in significance testing of hypotheses in the presence of nuisance parameters, J Am Stat Assoc 84 (406), 602-607, 1989.
  • [15] S. Weerahandi, Generalized Inference in Repeated Measures: Exact Methods in MANOVA and Mixed Models, John Wiley & Sons, 2004.
  • [16] S. Weerahandi, ANOVA under unequal error variances, Biometrics 51 (2), 589-599, 1995.
  • [17] S. Weerahandi, Generalized confidence intervals, J Am Stat Assoc 88 (423), 899-905, 1993.
  • [18] S. Weerahandi, Testing regression equality with unequal variances, Econometrica 55 (5), 1211-1215, 1987.
  • [19] S. Weerahandi and K. Krishnamoorthy, A note reconciling ANOVA tests under unequal error variances, Commun. Stat. Theory Methods 48 (3), 689-693, 2019.
  • [20] S. Weerahandi and C.R. Yu, Exact distributions of statistics for making inferences on mixed models under the default covariance structure, J. Stat. Distrib. Appl. 7 (4), 1-14, 2020.
  • [21] L. Xu, Parametric bootstrap approaches for two-way MANOVA with unequal cell sizes and unequal cell covariance matrices, J. Multivar. Anal. 133, 291-303, 2015.
  • [22] L. Xu, F. Yang, A. Abula and S. Qin, A parametric bootstrap approach for two-way ANOVA in presence of possible interactions with unequal variances, J. Multivar. Anal. 115, 172-180, 2013.
  • [23] J. Zhang, Two-way MANOVA with unequal cell sizes and unequal cell covariance matrices, Technometrics 53 (4), 426-439, 2011.

Two approaches to extend classical MANOVA tests to the unequal covariances case

Yıl 2023, Cilt: 52 Sayı: 4, 1066 - 1081, 15.08.2023

Samaradasa Weerahandi Malwane Ananda Osman Dağ

https://doi.org/10.15672/hujms.1176840

Öz

This article presents two approaches to extend classical MANOVA tests to the unequal covariances case. The first approach is illustrated by extending the classical Wilks test, which is valid only when covariances are equal. Such tests will be based on exact probabilities of certain extreme regions. We will also show how tests numerically equivalent to the parametric bootstrap tests could be easily obtained without using any bootstrap sampling arguments, so that resulting p-values are also based on exact probabilities of well defined extreme regions. Being systematic approaches, by taking similar approaches, researchers should be able to derive generalized tests in MANCOVA, higher-way MANOVA, and in RM MANOVA under heteroscedasticity, in which the parametric bootstrap type approaches run into difficulties.

Anahtar Kelimeler

Generalized inference parametric bootstrap generalized p-value fiducial inference

Kaynakça

  • [1] M.M.A. Ananda, O. Dag and S. Weerahandi, Heteroscedastic two-way ANOVA under constraints, Commun. Stat. Theory Methods, Doi:10.1080/03610926.2022.2059682, 2022.
  • [2] M.M.A. Ananda and S. Weerahandi, Two-Way ANOVA with unequal cell frequencies and unequal variances, Stat. Sin.7 (3), 631-646, 1997.
  • [3] S.C. Chow and S.G. Wang, Advanced Linear Models, Marcel Dekker, New York, 1994.
  • [4] Y. Fujikoshi, Two-way ANOVA models with unbalanced data, Discrete Math. 116 (1-3), 315-334, 1993.
  • [5] J. Gamage, T. Mathew and S.Weerahandi, Generalized p-values and generalized confidence regions for the multivariate BehrensFisher problem and MANOVA, J. Multivar. Anal. 88 (1), 177189, 2004.
  • [6] R.A. Johnson and S. Weerahandi, A Bayesian solution to the multivariate Behrens- Fisher problem, J Am Stat Assoc 83 (401), 145-149, 1988.
  • [7] R.A. Johnson and D.W. Wichern, Applied Multivariate Statistical Analysis, Prentice Hall Upper Saddle River, NJ, 2002.
  • [8] K. Krishnamoorthy and F. Lu, A parametric bootstrap solution to the MANOVA under heteroscedasticity, J Stat Comput Simul 80 (8), 873887, 2010.
  • [9] K. Krishnamoorthy, F. Lu and T. Mathew, A parametric bootstrap approach for ANOVA with unequal variances: fixed and random models, Comput Stat Data Anal 51 (12), 5731-5742, 2007.
  • [10] X. Li, J. Wang and H. Liang, comparison of several means: a fiducial based approach, Comput Stat Data Anal 55 (5), 1993-2002, 2011.
  • [11] A. Roy and A. Bose, coverage of generalized confidence intervals, J. Multivar. Anal. 100 (7), 1384-1397, 2009.
  • [12] S.M. Sadooghi-Alvandi, A.A. Jafari and H.A. Mardarni-Fard, One-way ANOVA with unequal variances, Commun. Stat. Theory Methods 41 (22), 42004221, 2012.
  • [13] A. Thomson and D. Randall-MacIver, The Ancient Races of the Thebaid: Being an Anthropometrical Study of the Inhabitants of Upper Egypt from the Earliest Prehistoric Times to the Mohammedan Conquest, Based Upon the Examination of Over 1,500 Crania, Clarendon Press, 1905.
  • [14] K. Tsui and S. Weerahandi, Generalized p-values in significance testing of hypotheses in the presence of nuisance parameters, J Am Stat Assoc 84 (406), 602-607, 1989.
  • [15] S. Weerahandi, Generalized Inference in Repeated Measures: Exact Methods in MANOVA and Mixed Models, John Wiley & Sons, 2004.
  • [16] S. Weerahandi, ANOVA under unequal error variances, Biometrics 51 (2), 589-599, 1995.
  • [17] S. Weerahandi, Generalized confidence intervals, J Am Stat Assoc 88 (423), 899-905, 1993.
  • [18] S. Weerahandi, Testing regression equality with unequal variances, Econometrica 55 (5), 1211-1215, 1987.
  • [19] S. Weerahandi and K. Krishnamoorthy, A note reconciling ANOVA tests under unequal error variances, Commun. Stat. Theory Methods 48 (3), 689-693, 2019.
  • [20] S. Weerahandi and C.R. Yu, Exact distributions of statistics for making inferences on mixed models under the default covariance structure, J. Stat. Distrib. Appl. 7 (4), 1-14, 2020.
  • [21] L. Xu, Parametric bootstrap approaches for two-way MANOVA with unequal cell sizes and unequal cell covariance matrices, J. Multivar. Anal. 133, 291-303, 2015.
  • [22] L. Xu, F. Yang, A. Abula and S. Qin, A parametric bootstrap approach for two-way ANOVA in presence of possible interactions with unequal variances, J. Multivar. Anal. 115, 172-180, 2013.
  • [23] J. Zhang, Two-way MANOVA with unequal cell sizes and unequal cell covariance matrices, Technometrics 53 (4), 426-439, 2011.
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular İstatistik
Bölüm İstatistik
Yazarlar

Samaradasa Weerahandi 0000-0003-2421-2860

Malwane Ananda 0000-0002-8585-5360

Osman Dağ 0000-0002-1750-8789

Yayımlanma Tarihi 15 Ağustos 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 52 Sayı: 4

Kaynak Göster

APA Weerahandi, S., Ananda, M., & Dağ, O. (2023). Two approaches to extend classical MANOVA tests to the unequal covariances case. Hacettepe Journal of Mathematics and Statistics, 52(4), 1066-1081. https://doi.org/10.15672/hujms.1176840
AMA Weerahandi S, Ananda M, Dağ O. Two approaches to extend classical MANOVA tests to the unequal covariances case. Hacettepe Journal of Mathematics and Statistics. Ağustos 2023;52(4):1066-1081. doi:10.15672/hujms.1176840
Chicago Weerahandi, Samaradasa, Malwane Ananda, ve Osman Dağ. “Two Approaches to Extend Classical MANOVA Tests to the Unequal Covariances Case”. Hacettepe Journal of Mathematics and Statistics 52, sy. 4 (Ağustos 2023): 1066-81. https://doi.org/10.15672/hujms.1176840.
EndNote Weerahandi S, Ananda M, Dağ O (01 Ağustos 2023) Two approaches to extend classical MANOVA tests to the unequal covariances case. Hacettepe Journal of Mathematics and Statistics 52 4 1066–1081.
IEEE S. Weerahandi, M. Ananda, ve O. Dağ, “Two approaches to extend classical MANOVA tests to the unequal covariances case”, Hacettepe Journal of Mathematics and Statistics, c. 52, sy. 4, ss. 1066–1081, 2023, doi: 10.15672/hujms.1176840.
ISNAD Weerahandi, Samaradasa vd. “Two Approaches to Extend Classical MANOVA Tests to the Unequal Covariances Case”. Hacettepe Journal of Mathematics and Statistics 52/4 (Ağustos 2023), 1066-1081. https://doi.org/10.15672/hujms.1176840.
JAMA Weerahandi S, Ananda M, Dağ O. Two approaches to extend classical MANOVA tests to the unequal covariances case. Hacettepe Journal of Mathematics and Statistics. 2023;52:1066–1081.
MLA Weerahandi, Samaradasa vd. “Two Approaches to Extend Classical MANOVA Tests to the Unequal Covariances Case”. Hacettepe Journal of Mathematics and Statistics, c. 52, sy. 4, 2023, ss. 1066-81, doi:10.15672/hujms.1176840.
Vancouver Weerahandi S, Ananda M, Dağ O. Two approaches to extend classical MANOVA tests to the unequal covariances case. Hacettepe Journal of Mathematics and Statistics. 2023;52(4):1066-81.

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