Symbolic Computation for Statistical Inference [Hardcover]

Over recent years, developments in statistical computing have freed statisticians from the burden of calculation and have made possible new methods of analysis that previously would have been too difficult or time-consuming. Up till now these developments have been primarily in numerical computation and graphical display, but equal steps forward are now being made in the area of symbolic computing: the use of computer languages and procedures to manipulate expressions. This allows researchers to compute analgebraic expression, rather than evaluate the expression numerically over a given range. This book summarizes a decade of research into the use of symbolic computation applied to statistical inference problems. It shows the considerable potential of the subject to automate statistical calculation, leaving researchers free to concentrate on new concepts. Starting with the development of algorithms applied to standard undergraduate problems, the book then goes on to develop increasingly more powerful tools. Later chapters then discuss the application of these algorithms to different areas of statistical methodology.

1. Introduction
2. Probability and random variables
3. Fundamental procedures
4. Asymptotic expansions
5. Expansions of expectations, cumulants, and unbiased estimates
6. Expansions of distributions
7. Expansions for likelihood quantities
8. The analytic bootstrap
9. Sample surveys
10. Intersection matrices