Multistep-Multiscale Bootstrap Resampling

Hidetoshi Shimodaira

Department of Mathematical and Computing Sciences

Tokyo Institute of Technology

Approximately unbiased tests based on the bootstrap probabilities are considered for the exponential family of distributions with unknown expectation parameter vector, where the null hypothesis is represented as an arbitrary-shaped region with smooth boundaries. The newly developed multistep-multiscale bootstrap resampling calculates an approximately unbiased p-value with asymptotic third-order accuracy.

This p-value is equivalent to those obtained by the double bootstrap (Hall 1992) and the p*-formula (Barndorff-Nielsen 1986), yet the implementation of the new algorithm leads to simpler and faster computation. In fact, the simplest form (one-step multiscale bootstrap) has been already used in Bioinformatics applications (Shimodaira 2002), and the paper (Shimodaira and Hasegawa 2001) for the software implementing the algorithm is highly cited.

The multistep-multiscale bootstrap resampling is described in Shimodaira (2004a) [PDF]. The technical details are given in Shimodaira (2004b) [PDF]. The main result is proved in Shimodaira (2003) [HTML], which is a computer program for Mathematica with MathTensor. The multiscale bootstrap of Shimodaira (2002) is a special case of the multistep-multiscale bootstrap, i.e., the one-step multiscale bootstrap.

The abstract is available in Japanese language Shimodaira (2004c) [PDF].  See Japanese page.

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