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Multivariate statistical outliers

Multivariate statistical outliers
Multivariate statistical outliers

Most of the extensive literature on outliers refers to the univariate case. This thesis takes up the topic of outliers in multivariate data, examining the performance of existing tests, and developing tests using other procedures and tests for specific data structures. Chapter 1 introduces key concepts and provides examples to illustrate some of the main themes. Chapter 2 comprises a full review of previous work on outliers in multivariate data. Wilks' test is examined in the third chapter. It is confirmed by simulation that the Bonferroni approximation used to provide percentage points is accurate for testing for one outlier, but not for two or more. Simulated percentage points are constructed for up to four outliers, for sample sizes up to 100 and up to 5 dimensions. Chapter 4 presents sequential application of Wilks' statistic based on Rosner's procedures for univariate statistics which control the error level of the test for different numbers of outliers. Chapter 5 examins Rohlf's test using distances in the minimum spanning tree. This is shown not to give a test with good properties. In Chapter 6, a two-outlier test is constructed by union-intersection methodology. This is sometimes more powerful than Wilks' test, but much less powerful under other data configurations. In Chapter 7, tests are derived for outliers in normal data with structured covariance matrices, specifically block structure and equicorrelation. It is shown by simulation that these tests are substantially more powerful than Wilks'. The final chapter examines outliers in the context of the multivariate linear model. Residuals are defined and the related topic of influence on estimates of regression coefficients is considered.

University of Southampton
Caroni-Richardson, Chrysseis
Caroni-Richardson, Chrysseis

Caroni-Richardson, Chrysseis (1990) Multivariate statistical outliers. University of Southampton, Doctoral Thesis.

Record type: Thesis (Doctoral)

Abstract

Most of the extensive literature on outliers refers to the univariate case. This thesis takes up the topic of outliers in multivariate data, examining the performance of existing tests, and developing tests using other procedures and tests for specific data structures. Chapter 1 introduces key concepts and provides examples to illustrate some of the main themes. Chapter 2 comprises a full review of previous work on outliers in multivariate data. Wilks' test is examined in the third chapter. It is confirmed by simulation that the Bonferroni approximation used to provide percentage points is accurate for testing for one outlier, but not for two or more. Simulated percentage points are constructed for up to four outliers, for sample sizes up to 100 and up to 5 dimensions. Chapter 4 presents sequential application of Wilks' statistic based on Rosner's procedures for univariate statistics which control the error level of the test for different numbers of outliers. Chapter 5 examins Rohlf's test using distances in the minimum spanning tree. This is shown not to give a test with good properties. In Chapter 6, a two-outlier test is constructed by union-intersection methodology. This is sometimes more powerful than Wilks' test, but much less powerful under other data configurations. In Chapter 7, tests are derived for outliers in normal data with structured covariance matrices, specifically block structure and equicorrelation. It is shown by simulation that these tests are substantially more powerful than Wilks'. The final chapter examines outliers in the context of the multivariate linear model. Residuals are defined and the related topic of influence on estimates of regression coefficients is considered.

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Published date: 1990

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Local EPrints ID: 461841
URI: http://eprints.soton.ac.uk/id/eprint/461841
PURE UUID: 5c4df1d3-eed6-4e95-91f3-c62052bacabd

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Date deposited: 04 Jul 2022 18:57
Last modified: 04 Jul 2022 20:28

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Author: Chrysseis Caroni-Richardson

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