Sankhya: The Indian Journal of Statistics

1994, Volume 56, Series B, Pt. 1, pp. 121--126

ON THE ASYMPTOTIC PRECISION OF THE WELCH APPROACH

By

R. ARDANUY and J. F. LOPEZ, *Universidad de Salamanca*

SUMMARY. In this paper we attempt to investigate the order of accuracy in Welch type approximations of the distributions of certain studentized statistics. We compare the exact cumulative distribution function of statistic $T = \frac{X-{\theta}}{\sqrt{\sum{\lambda}_{i} S_2^{i}}}$ with the value obtained by means of Welch approximation. The main result is that this difference is *O _{p}(f^{-3/2})* and also

*AMS subject classification.* 62F05, 62F03, 62E20.

*Key words and phrases.* Asymptotic properties of tests, Behrens-Fisher problem, difference of means, hypothesis testing, Welch approximation.