LIKELIHOOD ANALYSIS FOR THE DIFFERENCE IN MEANS OF TWO INDEPENDENT NORMAL DISTRIBUTIONS WITH ONE VARIANCE UNKNOWN
Keywords:
Behrens-Fisher problem, Canonical parameter, Modied signed log-likelihood ratio statistics, Satterthwaite.Abstract
Maity and Sherman (2006) considered the situation in two-sample testing for the
dierence in means when one variance is assumed to be known while the other
variance is treated as unknown. This problem arises in many real life situations,
for example, when one is interested in comparing a standard treatment with a
new treatment in medical studies. The variance for the standard treatment is
assumed to be known from historical data, and the variance for the new treatment
is unknown. Following the argument in Satterthwaite (1941, 1946), Maity
and Sherman (2006) obtained the condence interval for the dierence in means
based on an approximate t-distribution. In this paper, a likelihood-based third
order asymptotic method is introduced to obtain the condence intervals for the
dierence in means. Simulations are used to show that the proposed method has
better coverage property than Maity and Sherman's t-method, especially when
the sample sizes are small.
