In a pre-post or other kind of repeated measures study, it is sometimes clear that the mean profiles of the repeated measures are parallel across treatment groups. When for example, it can be assumed that there is no interaction between the repeated measure factor and the treatment, it would be of interest to know how much of a difference exists in the effect of the treatments. Such differences in the absence of interaction are referred to as level differences. In this paper, we consider methods for constructing confidence regions for level differences in the multi-dimensional cases. We derive asymptotic expansions for some intuitively appealing pivotal quantities to construct the confidence regions corrected up to the second order. Such corrections are shown in the multivariate literature to improve the accuracy of asymptotic approximations. We evaluate the finite sample performance of the confidence regions via a simulation study. Real-data example from forestry is used to provide an empirical illustration of the features of the various confidence regions proposed in the paper.
|Number of pages||14|
|Journal||Journal of Statistical Planning and Inference|
|State||Published - Aug 1 2016|
Bibliographical noteFunding Information:
The research reported in this paper was supported by the National Natural Science Foundation of China (grant 11271134) and the 111 Project (B14019) of Chinese Ministry of Education. The research of Solomon W. Harrar was conducted during his research visit at East China Normal University from January 1 to March 31, 2014. He is grateful to the University of Kentucky and East China Normal University for making this visit possible. The authors would like to thank the anonymous referee and the associate editor for critically reading the manuscript and providing valuable suggestions.
© 2016 Elsevier B.V.
- Asymptotic expansion
- Bartlett's correction
- Characteristic function
- Profile analysis
- Repeated measures
- Wald's criteria
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics