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An exact test for equality of two normal mean vectors with monotone missing data

Yıl 2022, Cilt: 51 Sayı: 4, 1211 - 1218, 01.08.2022
https://doi.org/10.15672/hujms.871588

Öz

The problem of testing equality of two normal mean vectors with incomplete data when the covariance matrices are equal is considered. For data matrices with monotone missing pattern, an exact test is proposed as an alternative one to the traditional likelihood ration test. Numerical power comparisons show that the powers of the proposed test and the likelihood ration test are comparable. However, the proposed test is an exact one. It is easy to use and useful to identify the component that caused the rejection of null hypothesis. It is illustrated using an example.

Destekleyen Kurum

NSFC

Kaynakça

  • [1] T.W. Anderson, Maximum likelihood estimates for a multivariate normal distribution when some observations are missing, J. Amer. Statist. Assoc. 52 (278), 200-203, 1957.
  • [2] R. Bhargava, Multivariate tests of hypotheses with incomplete data, PhD Thesis, Stanford University, 1962.
  • [3] J. Hao and K. Krishnamoorthy, Inferences on normal covariance matrix and generalized variance with incomplete data, J. Multivariate Anal. 78 (1), 62-82, 2001.
  • [4] T. Kanda and Y. Fujikoshi, Some basic properties ofthe MLE’s for a multivariate normal distribution with monotone missing data, Amer. J. Math. Management Sci. 18 (1–2), 161-190, 1998.
  • [5] K. Krishnamoorthy and M. Pannala, Some simple test procedures for normal mean vector with incomplete data, Ann. Inst. Statist. Math. 50 (3), 531-542, 1998.
  • [6] K. Krishnamoorthy and M. Pannala, Confidence estimation of normal mean vector with incomplete data, Canad. J. Statist. 27 (2), 395-407, 1999.
  • [7] K. Krishnamoorthy and J. Yu, Multivariate Behrens-Fisher problem with missing data, J. Multivariate Anal. 105 (1), 141-150, 2012.
  • [8] R.J.A. Little, A test of missing completely at random for multivariate data with missing values, J. Amer. Statist. Assoc. 83 (404), 1198-1202, 1988.
  • [9] R.J.A. Little and D.B. Rubin, Statistical Analysis with Missing Data, Wiley, New York, 1987.
  • [10] G.B. Lu and J.B. Copas, Missing at random, likelihood ignorability and model completeness, Ann. Statist. 32 (2), 754-765, 2004.
  • [11] G.J. McLachlan and T. Krishnan, The EM Alxorithm and Extensions, 4th ed., Wiley, New York, 1997.
  • [12] N. Seko, T. Kawasaki and T. Seo, Testing equality of two mean vectors with two-step monotone missing data, Amer. J. Math. Management Sci. 31 (1), 117-135, 2011.
  • [13] N. Shutoh, M. Kusumi, W. Morinaga, S. Yamada and T. Seo, Testing equality of mean vectors in two sample problems with missing data, Comm. Statist. Simulation Comput. 39 (3), 487-500, 2010.
  • [14] M.S. Srivastava, Multivariate data with missing observations, Comm. Statist. Theory Methods 14 (4), 775-792, 1985.
  • [15] M.S. Srivastava and E.M. Carter, The maximum likelihood method for non-response in sample survey, Surv. Methodol. 12, 61-72, 1986.
  • [16] A. Yagi and T. Seo, Tests for equality of mean vectors and simultaneous confidence intervals with two-step or three-step monotone missing data patterns, Amer. J. Math. and Management Sci. 34 (3), 213-233, 2015.
  • [17] J. Yu, K. Krishnamoorthy and M. Pannala, Two-sample inference for normal mean vectors based on monotone missing data, J. Multivariate Anal. 97 (10), 2162-2176, 2006.
Yıl 2022, Cilt: 51 Sayı: 4, 1211 - 1218, 01.08.2022
https://doi.org/10.15672/hujms.871588

Öz

Kaynakça

  • [1] T.W. Anderson, Maximum likelihood estimates for a multivariate normal distribution when some observations are missing, J. Amer. Statist. Assoc. 52 (278), 200-203, 1957.
  • [2] R. Bhargava, Multivariate tests of hypotheses with incomplete data, PhD Thesis, Stanford University, 1962.
  • [3] J. Hao and K. Krishnamoorthy, Inferences on normal covariance matrix and generalized variance with incomplete data, J. Multivariate Anal. 78 (1), 62-82, 2001.
  • [4] T. Kanda and Y. Fujikoshi, Some basic properties ofthe MLE’s for a multivariate normal distribution with monotone missing data, Amer. J. Math. Management Sci. 18 (1–2), 161-190, 1998.
  • [5] K. Krishnamoorthy and M. Pannala, Some simple test procedures for normal mean vector with incomplete data, Ann. Inst. Statist. Math. 50 (3), 531-542, 1998.
  • [6] K. Krishnamoorthy and M. Pannala, Confidence estimation of normal mean vector with incomplete data, Canad. J. Statist. 27 (2), 395-407, 1999.
  • [7] K. Krishnamoorthy and J. Yu, Multivariate Behrens-Fisher problem with missing data, J. Multivariate Anal. 105 (1), 141-150, 2012.
  • [8] R.J.A. Little, A test of missing completely at random for multivariate data with missing values, J. Amer. Statist. Assoc. 83 (404), 1198-1202, 1988.
  • [9] R.J.A. Little and D.B. Rubin, Statistical Analysis with Missing Data, Wiley, New York, 1987.
  • [10] G.B. Lu and J.B. Copas, Missing at random, likelihood ignorability and model completeness, Ann. Statist. 32 (2), 754-765, 2004.
  • [11] G.J. McLachlan and T. Krishnan, The EM Alxorithm and Extensions, 4th ed., Wiley, New York, 1997.
  • [12] N. Seko, T. Kawasaki and T. Seo, Testing equality of two mean vectors with two-step monotone missing data, Amer. J. Math. Management Sci. 31 (1), 117-135, 2011.
  • [13] N. Shutoh, M. Kusumi, W. Morinaga, S. Yamada and T. Seo, Testing equality of mean vectors in two sample problems with missing data, Comm. Statist. Simulation Comput. 39 (3), 487-500, 2010.
  • [14] M.S. Srivastava, Multivariate data with missing observations, Comm. Statist. Theory Methods 14 (4), 775-792, 1985.
  • [15] M.S. Srivastava and E.M. Carter, The maximum likelihood method for non-response in sample survey, Surv. Methodol. 12, 61-72, 1986.
  • [16] A. Yagi and T. Seo, Tests for equality of mean vectors and simultaneous confidence intervals with two-step or three-step monotone missing data patterns, Amer. J. Math. and Management Sci. 34 (3), 213-233, 2015.
  • [17] J. Yu, K. Krishnamoorthy and M. Pannala, Two-sample inference for normal mean vectors based on monotone missing data, J. Multivariate Anal. 97 (10), 2162-2176, 2006.
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular İstatistik
Bölüm İstatistik
Yazarlar

Jianqi Yu 0000-0002-1273-4066

Bin Wang 0000-0001-9944-2551

Tao Zhang Bu kişi benim 0000-0002-8135-5000

Yayımlanma Tarihi 1 Ağustos 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 51 Sayı: 4

Kaynak Göster

APA Yu, J., Wang, B., & Zhang, T. (2022). An exact test for equality of two normal mean vectors with monotone missing data. Hacettepe Journal of Mathematics and Statistics, 51(4), 1211-1218. https://doi.org/10.15672/hujms.871588
AMA Yu J, Wang B, Zhang T. An exact test for equality of two normal mean vectors with monotone missing data. Hacettepe Journal of Mathematics and Statistics. Ağustos 2022;51(4):1211-1218. doi:10.15672/hujms.871588
Chicago Yu, Jianqi, Bin Wang, ve Tao Zhang. “An Exact Test for Equality of Two Normal Mean Vectors With Monotone Missing Data”. Hacettepe Journal of Mathematics and Statistics 51, sy. 4 (Ağustos 2022): 1211-18. https://doi.org/10.15672/hujms.871588.
EndNote Yu J, Wang B, Zhang T (01 Ağustos 2022) An exact test for equality of two normal mean vectors with monotone missing data. Hacettepe Journal of Mathematics and Statistics 51 4 1211–1218.
IEEE J. Yu, B. Wang, ve T. Zhang, “An exact test for equality of two normal mean vectors with monotone missing data”, Hacettepe Journal of Mathematics and Statistics, c. 51, sy. 4, ss. 1211–1218, 2022, doi: 10.15672/hujms.871588.
ISNAD Yu, Jianqi vd. “An Exact Test for Equality of Two Normal Mean Vectors With Monotone Missing Data”. Hacettepe Journal of Mathematics and Statistics 51/4 (Ağustos 2022), 1211-1218. https://doi.org/10.15672/hujms.871588.
JAMA Yu J, Wang B, Zhang T. An exact test for equality of two normal mean vectors with monotone missing data. Hacettepe Journal of Mathematics and Statistics. 2022;51:1211–1218.
MLA Yu, Jianqi vd. “An Exact Test for Equality of Two Normal Mean Vectors With Monotone Missing Data”. Hacettepe Journal of Mathematics and Statistics, c. 51, sy. 4, 2022, ss. 1211-8, doi:10.15672/hujms.871588.
Vancouver Yu J, Wang B, Zhang T. An exact test for equality of two normal mean vectors with monotone missing data. Hacettepe Journal of Mathematics and Statistics. 2022;51(4):1211-8.