A sieve bootstrap two-sample t-test under serial correlation

The classical two-sample t-test assumes that observations are independent. A violation of this assumption could lead to unreliable or even erroneous conclusions. However, in many biological studies, data are recorded over time and hence exhibit serial correlation. In order to take such temporal dependence into account, we suggest applying the sieve bootstrap method to generate replications of the observed data and then using these proxy-dependent processes to construct the empirical distribution for the t-statistic. The proposed method is fast, distribution-free, and well approximates the nominal significance level. We illustrate our approach in application to detection problem of brain activity in functional magnetic resonance imaging (fMRI) and a longitudinal study of weight growth in rats.