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Computer intensive statistical methods: validation, model selection and bootstrap. (English) Zbl 0829.62001

London: Chapman & Hall. x, 263 p. (1994).
The book presents computer intensive statistical methods. 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 analytical treatment. The new effects caused by all this computation can be approached by a further round of computations as in validation and bootstrap methods is done. The large interest in computer intensive methods in statistics comes from the information concept. The purpose is to take care of and present the information in the given data as efficiently as possible, but this typically requires computations which are heavy to do by hand.
Much statistical software is now available and easy to use without much theoretical knowledge. Some frequent misuses of classical statistical software can be counteracted by computer intensive methods and these possibilities in model selection situations are in particular discussed in the book.
After a Prelude in Chapter 1, the computer intensive philosophy is explained in Chapter 2. The computer intensive philosophy, based on data base variations, is complementary to the classical philosophy of statistics, based on sample space models. The classical well structured problems naturally have to be handled by the traditional methods, and complex and less structured problems by the computer intensive methods. Examples of problems which can be approached by the new methods are: model selection, anything calculated from uncertain data, classification, image analysis, interpretation of satellite data, time series, factor analysis, etc.
In Chapter 3 the cross-validation method of evaluating given models is discussed. Chapter 4 deals with the validation of time series problems. In Chapter 5 the very general bootstrap method – the concept of which had been introduced in 1979 [B. Efron, Ann. Stat. 7, 1-26 (1979; Zbl 0406.62024)] and having enormous success since then – is introduced. In Chapter 6 further bootstrap results are discussed and Chapter 7 deals with computer intensive applications of validation and bootstrap methods. References and Index close the book.

MSC:

62-02 Research exposition (monographs, survey articles) pertaining to statistics
62G09 Nonparametric statistical resampling methods
65C99 Probabilistic methods, stochastic differential equations
68U99 Computing methodologies and applications

Citations:

Zbl 0406.62024
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