A. Wong and Y. Wu, “Likelihood Analysis for the Difference in Means of Two Independent Normal Distributions with One Variance Unknown,” Journal of Statistical Research, Vol. 42, 2008, pp. 17-35.

has been cited by the following article:

• TITLE: Revisit the Two Sample t-Test with a Known Ratio of Variances

  AUTHORS: Yongxiu She, Augustine Wong, Xiaofeng Zhou

  KEYWORDS: Behrens-Fisher Problem, Canonical Parameter, Exponential Family Model, Likelihood Based Inference, Modified Signed Log-Likelihood Ratio Statistic, Satterthwaite Method.

  JOURNAL NAME: Open Journal of Statistics, Vol.1 No.3, October 20, 2011

  ABSTRACT: Inference for the difference of two independent normal means has been widely studied in staitstical literature. In this paper, we consider the case that the variances are unknown but with a known relationship between them. This situation arises frequently in practice, for example, when two instruments report averaged responses of the same object based on a different number of replicates, the ratio of the variances of the response is then known, and is the ratio of the number of replicates going into each response. A likelihood based method is proposed. Simulation results show that the proposed method is very accurate even when the sample sizes are small. Moreover, the proposed method can be extended to the case that the ratio of the variances is unknown.