A new procedure for the Behrens-Fisher Problem that guarantees confidence levels

被引：1
作者：
Hayter A.J. [1 ]
机构：
[1] Department of Business Information and Analytics, University of Denver, Denver
来源：
Journal of Statistical Theory and Practice | 2013年 / 7卷 / 3期
关键词：
Acceptance set; Behrens-Fisher; Beta distribution; Confidence interval; Confidence set; Normal distribution; p; -Value; Pairwise comparison; Test procedure; Unequal variances;
D O I：
10.1080/15598608.2013.790239
中图分类号：
学科分类号：
摘要：
This article considers the Behrens-Fisher problem of comparing two independent normal means without making any assumptions about the two unknown population variances. It is known that the natural statistic for this problem has a distribution that depends upon the ratio of the two variances, and that inferences can be made by using a t-distribution with degrees of freedom equal to the minimum of the degrees of freedom of the two variance estimates. This is the limiting distribution of the statistic as the variance ratio tends to zero or one. In this article a new procedure is developed that simultaneously provides inferences on both the means and the variance ratio. This procedure bounds the variance ratio away from zero and infinity, so it can allow inferences on the means that are sharper than those provided by the limiting distribution. Some numerical illustrations of the advantage provided by this new procedure are presented. Copyright © 2013 Grace Scientific Publishing, LLC.
引用
收藏
页码：515 / 536
页数：21
相关论文
共 13 条
  • [1] Behrens, W.V., Ein beitrag zur Fehlerberechnung bei wenigen Beobachtungen (A contribution to error estimation with few observations) (1929) Landwirts. Jahrbcher, 68, p. 80737
  • [2] Chang, C.H., Pal, N., A revisit to the behrens-fisher problem: Comparison of five test methods (2008) Commun. Stat. Simulation Comput, 37 (6), pp. 1064-1085
  • [3] Fisher, R.A., The fiducial argument in statistical inference (1935) Ann. Eugenics, 8, pp. 391-398
  • [4] Huang, P., Tilley, B.C., Woolson, R.F., Lipsitz, S., Adjusting o'brien's test to control type i error for the generalized nonparametric behrens-fisher problem (2005) Biometrics, 61 (2), pp. 532-539
  • [5] Hsu, P.L., Contributions to the theory of "student's" t-Test as applied to the problem of two samples (1938) Statistical Research Memoris, 2, pp. 1-24. , London, UK, Department of Statistics, University College
  • [6] Kabaila, P., Tuck, J., Confidence intervals utilizing prior information in the behrens-fisher problem (2008) Austr. N. Z. J. Stat, 50 (4), pp. 309-328
  • [7] Mickey, M.R., Brown, M.B., Bounds on the distribution functions of the Behrens-Fisher statistic (1966) Ann. Math. Stat, 37, pp. 639-642
  • [8] Neubert, K., Brunner, E., A studentized permutation test for the non-parametric Behrens-Fisher problem (2007) Comput. Stat. Data Anal, 51 (10), pp. 5192-5204
  • [9] Ramos, P.D., Ferreira, D.F., A bayesian solution to the multivariate behrens-fisher problem (2010) Comput. Stat. Data Anal, 54 (6), pp. 1622-1633
  • [10] Satterthwaite, F.E., An approximate distribution of estimates of variance components (1946) Biometrics Bull, 2, pp. 110-114
12