Undercoverage of Wavelet-based Bootstrap Confidence Intervals for a Mean Difference

摘要

The decorrelating property of the discrete wavelet transformation (DWT) appears to be a valuable feature that avoids estimating the correlation structure in the original data space by bootstrap resampling the DWT. Data analysts have been using these so-called wavestrap methods in recent years without theoretical or empirical proof of their validity. However, our simulation studies show that these wavestraps yield undercoverage of parameters of interest for a mean difference. Thus, the wavestrap method is not preferred in obtaining resamples related to mean structure and should be used with caution. The reasons for these undercoverages are also discussed in this paper.