asymptotic analysis of the bootstrap methods 20030721
Department of Mathematical and Computing Sciences
Tokyo Institute of Technology
Ookayama, Meguro, Tokyo 152-8552, JAPAN.
shimo (a) is.titech.ac.jp
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.