- Hacettepe Journal of Mathematics and Statistics
- Vol: 31
- A BAYESIAN METHOD TO DETECT OUTLIERS IN MULTIVARIATE LINEAR REGRESSION
A BAYESIAN METHOD TO DETECT OUTLIERS IN MULTIVARIATE LINEAR REGRESSION
Authors : Ufuk Ekiz
Pages : 77-82
View : 14 | Download : 8
Publication Date : 2001-12-01
Article Type : Research
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 discussedKeywords : Realized error, posterior distribution, multivariate linear regression, Jeffrey's prior