Hawkins D.M. Identification of Outliers

Springer, 1980. — 195 p.The problem of outliers is one of the oldest in statistics, and during the last century and a half interest in it has waxed and waned several times. Currently it is once again an active research area after some years of relative neglect, and recent work has solved a number of old problems in outlier theory, and identified new ones. The major results are, however, scattered amongst many journal articles, and for some time there has been a clear need to bring them together in one place. That was the original intention of this monograph: but during execution it became clear that the existing theory of outliers was deficient in several areas, and so the monograph also contains a number of new results and conjectures.
In view of the enormous volume of literature on the outlier problem and its cousins, no attempt has been made to make the coverage exhaustive. The material is concerned almost entirely with the use of outlier tests that are known (or may reasonably be expected) to be optimal in some way. Such topics as robust estimation are largely ignored, being covered more adequately in other sources. The numerous ad hoc statistics proposed in the early work on the grounds of intuitive appeal or computational simplicity also are not discussed in any detail.
The main emphasis of the monograph is on the salient theoretical aspects of the problem, but the appendices of fractiles of many of the tests discussed will also be of use to practitioners interested in applying outlier tests to data.General theoretical principles
A single outlier in normal samples
The gamma distribution
Multiple outliers
Non-parametric tests
Outliers from the linear model
Multivariate outlier detection
Bayesian approach to outliers
Miscellaneous topics
Appendices
Fractiles of B and B^* for normal samples
Fractiles of L_k for normal samples
Fractiles of E_k for normal samples
Fracticles of T_n:l for normal samples
Fractiles for testing for two outliers in normal data
Probabilities of the Mosteller test
Fractiles of the Doornbos test
Fractiles of the Wilks statistics
Fractiles of X_(n)/W for samples from the chi-squared distribution
A single outlier in a two-way factorial experiment
Fractiles of X_(n) for the Poisson, binomial and negative binomial distributions.