Computer Intensive Statistical Methods: Validation, Model Selection, and Bootstrap PDF

The advance of computation has put statistics in a new perspective. Idealized model assumptions can now be replaced by more realistic modelling or by more or less model free analyses. Much statistical work and data analysis is now made by computers in ways that are too complicated for realistic analytical treatment. Automatic model selection poses for example new statistical questions which have been around for some time, but which recently have found working solutions. The statistical properties of the results from these and other extensive computations may well be different from the results from classical analyses. These problems are present in most regression and time series modelling and also in classification, clustering and the like. The new eflfects caused by all this computation can be approached by a further round of computations as we do in validation and bootstrap methods. Probably this is the only general way to proceed, but the methods will of course continue to be developed.

The enormous success of bootstrap methodology shows that many tricky problems have awaited something different and have now found a useful approach. Another good reason for the interest is that these methods are both amusing and theoretically appealing.

Classically educated statisticians should take a close look at these methods, and the young generation will certainly be handicapped without them.

This work benefits from theoretical work by many persons. Hopefully I have covered the most important contributions by the given references but I have not attempted to give a complete list of the work in the field. Instead I have referred to the work that fits into the line of this text, and have tried to keep methods and descriptions as easy as possible, as long as possible, to make the text readable for the widest possible audience. This is for example the reason why elementary confidence interval methods are presented in Chapter 5 and come back together with more advanced methods in Chapter 6, where more difficult material is collected.

I want to thank some colleagues and research students for their contributions. Ola Junghard, Anders Nordgaard, Elisabet Schmeling, Charlotte Karlsson, Lars Holmqvist, and Lars Haggmark SMHI have all applied or developed methods used in this text.

The Royal Statistical Society permitted the reproduction of material from Applied Statistics (Hjorth and Holmqvist, 1981), Professor Bradley Efron let me use one of his tables, not to mention aU the ideas I took without permission, and Professor Sture Holm allowed me to use material from a regression bootstrap paper to appear. I hope nobody else will find their central ideas here without proper references, but sometimes the same ideas pop up independently at about the same time.

A special thanks is due to the Swedish Transport Research Board for their interest in theoretical development for applications in traffic science and for their financial support in the important last stage of this work.

Author: J. S. Urban. Hjorth