Identification of OutliersSpringer Science & Business Media, 17.04.2013 - 188 Seiten 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 ofliterature 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. |
Inhalt
Multiple outliers | 22 |
The gamma distribution | 45 |
1 | 51 |
Appendix 2 | 54 |
Appendix 4 | 72 |
Nonparametric tests | 74 |
Outliers from the linear model | 95 |
4 | 102 |
Bayesian approach to outliers | 117 |
Probabilities of the Mosteller test | 155 |
BA A A B | 158 |
Appendix 9 | 163 |
A single outlier in a twoway factorial | 174 |
185 | |
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Häufige Begriffe und Wortgruppen
alternative analysis of variance Annals of Mathematical Anova Appendix approach asymptotic B₁ backward elimination Bayesian beta distribution binomial Biometrika Bonferroni approximation Bonferroni's inequality bound computed conservative fractiles contaminants cumulative distribution function degrees of freedom denote density detection Doornbos estimate forward selection fractiles gamma distribution given H₁ Hawkins inliers known linear model linear transformations masking effect Mathematical Statistics matrix Mosteller multiple comparison multiple outliers multivariate non-parametric normal distribution null hypothesis number of outliers optimal test order statistics outlier statistic outlier test outliers are present parameters principal component residuals priori probability procedure provides ranks recursive residuals regression rejection significance level simulation single outlier situation slippage problem slippage test slipped populations stepwise sufficient statistics Suppose suspected outliers t-distribution T₁ T₂ Technometrics test statistic theory Tietjen tolerance regions type I error univariate unknown values variables vector X₁