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)

Asymptotic Analysis of the Bootstrap Methods

This documentation consists of three parts, namely "Exponential Family of Distributions", "Tube-Coordinates and [Graphics:Images/index_gr_1.gif]-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 [Graphics:Images/index_gr_2.gif] terms ignoring the error of [Graphics:Images/index_gr_3.gif]. We use "o" to indicate [Graphics:Images/index_gr_4.gif] quantities. So, [Graphics:Images/index_gr_5.gif] indicates [Graphics:Images/index_gr_6.gif] and [Graphics:Images/index_gr_7.gif] indicates [Graphics:Images/index_gr_8.gif], etc. We repeatedly use a simplification function to keep only up to [Graphics:Images/index_gr_9.gif] 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.

Exponential Family of Distributions

Tube-Coordinates and [Graphics:Images/index_gr_1387.gif]-formula

Bootstrap Methods

Converted by Mathematica      July 21, 2003