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.
shimo (a) is.titech.ac.jp
http://www.is.titech.ac.jp/~shimo/
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.