asymptotic analysis of the bootstrap methods 20030721

Hidetoshi Shimodaira

Department of Mathematical and Computing Sciences
Tokyo Institute of Technology
Ookayama, Meguro, Tokyo 152-8552, JAPAN.

EMAIL: shimo@is.titech.ac.jp
URL: http://www.is.titech.ac.jp/~shimo/

Asymptotic Analysis of the Bootstrap Methods

This documentation consists of three parts, namely "Exponential Family of Distributions", "Tube-Coordinates and -formula", and "Bootstrap Methods".  Each part is an independent Mathematica session, and should be run separately.

The calculation is third-order accurate, correct  up to terms ignoring the error of . We use "o" to indicate quantities. So, indicates and indicates , etc. We repeatedly use a simplification function to keep only up to terms.

In the first two parts, the tensor notation is heavily used. The add-on package "MathTensor" is required to run the Mathematica session by yourself.