Behrens-Fisher Problem with One Variance Unknown

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





References:
<p>[1] A. Maity, and M. Sherman, &ldquo;The Two Sample T-test with One Variance
Unknown&rdquo;, The American Statistician, Vol. 60, No.2, pp. 163-166, 2006.
[2] F.E. Satterthwaite, &ldquo;Synthesis of variance&rdquo;, Psychometrik, Vol. 6, pp. 309-
316, 1941.
[3] F.E. Satterthwaite, &ldquo;An approximate distribution of estimates of variance
components&rdquo;, Biometric Bulletin, Vol. 6, pp. 110-114, 1946.
[4] S. Niwitpong, &ldquo;Confidence intervals for the difference of two normal
population means with one variance unknown&rdquo;, Thailand Statistician, Vol.
7, pp. 161-177, 2009.
[5] 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.
[6] S. Weerahandi, &ldquo;Exact Statistical Methods for Data Analysis&rdquo;, Springer,
NewYork, 1995.
[7] 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.
[8] 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>