A BAYESIAN METHOD TO DETECT OUTLIERS IN MULTIVARIATE LINEAR REGRESSION

Year 2002, Volume: 31, 77 - 82, 01.12.2001

Ufuk Ekiz

Abstract

In this study, a Bayesian method will be introduced to describe outlying

observations in multivariate linear regression. This method was proposed by

Chaloner and Brant [3]. Later on, Varbanov [7] extended this method to

apply to multivariate linear regression. According to Chaloner and Brant,

an observation will be accepted as an outlier if the following condition is ful-

filled: the posterior probability of the occurrence of the realized error (Arnold

Zelner [8]) of an observation being greater than a critical value "k", is higher

than the probability an error occurred in the model, with a critical value

"k" over the assumed distribution. That is, if $pr[(\epsilon_i/sigma, y) > k] > pr(\epsilon_i > k)$

then the $i^{th}$ observation will be accepted as an outlier. In the second section,

the method proposed by Varbanov [7] will be considered. In the application

section the existence or non-existence of outlying observations over the pos-

terior distribution of the square form of the realized error in multivariate

linear regression data is discussed

Keywords

Realized error, posterior distribution, multivariate linear regression, Jeffrey's prior

References

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