Undercoverage of Wavelet-Based Resampling Confidence Intervals

The decorrelating property of the discrete wavelet transformation (DWT) appears valuable because one can avoid estimating the correlation structure in the original data space by bootstrap resampling of the DWT. Several authors have shown that the wavestrap approximately retains the correlation structure of observations. However, simply retaining the same correlation structure of original observations does not guarantee enough variation for regression parameter estimators. Our simulation studies show that these wavestraps yield undercoverage of parameters for a simple linear regression for time series data of the type that arise in functional MRI experiments. It is disappointing that the wavestrap does not even provide valid resamples for both white noise sequences and fractional Brownian noise sequences. Thus, the wavestrap method is not completely valid in obtaining resamples related to linear regression analysis and should be used with caution for hypothesis testing as well. The rea...

• Type: Journal
• Year: 2008
• Where: CSSC
• Authors: Liansheng Tang, Wayne A. Woodward, William R. Schucany
• Keywords: Correlation Structure, CSSC 2008, Linear Regression, Noise Sequences