Some problems related to the rejection of outlying observations
Fieller, N. R. J.
Thesis or dissertation
- © 1976 N R J Fieller. All rights reserved. No part of this publication may be reproduced without the written permission of the copyright holder.
The thesis consists of six chapters. The introductory first chapter considers some of the more general problems involved in the detection and rejection of outlying observations, and.describes the general form of the tests discussed in detail in the later chapters.
In Chapter 2. likelihood-based criteria are derived for testing for single and multiple outliers at both the upper and the lower ends of samples from gamma distributions. The null distributions of these criteria are obtained by use of a recursive algorithm and the methods are extended to criteria appropriate for testing for multiple outliers occurring at both ends of the sample and to various 'Dixon' criteria. The results are applied to some practical examples.
In Chapter 3 likelihood-based tests and criteria for single outliers in univariate normal samples are considered. The null distributions of the criteria are obtained by recursive algorithms. The cases of known and unknown mean and variance are considered separately and the methods are extended to cases where independent estimates of the variance are available. These methods and results are extended in Chapter 4 to tests and criteria for multiple outliers in univariate normal samples. The extensions of the results of both of these chapters to single and multiple outliers in multivariate normal samples are considered in Chapter 6.
In Chapter 5 problems of single and multiple outliers in data following a linear model are discussed. A likelihood-based criterion is derived and the extreme tail of the null distribution of this criterion is obtained. Some practical examples on data from a series of chemical experiments are given.
- Department of Mathematical Statistics, The University of Hull
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