Upper Bound of the Generalize p-Value for the Behrens-Fisher Problem with a Known Ratio of Variances

This paper presents the generalized p-values for testing the Behrens-Fisher problem when a ratio of variance is known. We also derive a closed form expression of the upper bound of the proposed generalized p-value.





References:
<p>[1] E. Schechtman, and M. Sherman, &ldquo;The two-sample t-test with a known
ratio of Variances&rdquo;, Statistical Methodology, Vol.4, pp. 508-514, 2007.
[2] F.E. Satterthwaite, &ldquo;An approximate distribution of estimates of variance
components&rdquo;, Biometric Bulletin, Vol.6, pp. 110-114, 1946.
[3] S. Niwitpong, and Sa. Niwitpong, &ldquo;Confidence interval for the difference
of two normal population means with a known ratio of variances&rdquo;, Applied
Mathematical Sciences, Vol.4, pp. 347359, 2010.
[4] B.L. Welch, &ldquo;The significance of the difference between two means when
the population variances are unequal&rdquo;, Biometrika, Vol.29, pp. 350-362,
1983.
[5] S. Weerahandi, &ldquo;Exact Statistical Methods for Data Analysis&rdquo;, Springer,
NewYork, 1995.
[6] K-W. Tsui, and S. Weerahandi, &ldquo;Generalized p-values in significance
testing of hypotheses in the presence of nuisance parameters&rdquo;, J. Amer
Statist Assoc, Vol.84, pp. 60207, 1989.
[7] S. Tang,and K-W. Tsui, &ldquo;Distributional properties for the generalized
p-value for the BehrensFisher problem&rdquo;, Statistics Probability Letters,
Vol.77, pp. 18, 2007.</p>