A BAYESIAN METHOD TO DETECT OUTLIERS IN MULTIVARIATE LINEAR REGRESSION

Authors : Ufuk EKİZ

Pages : 77-82

View : 22 | Download : 6

Publication Date : 2001-12-01

Article Type : Research Paper

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 insert ignore into journalissuearticles values(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 $pr[insert ignore into journalissuearticles values(\epsilon_i/sigma, y); > k] > prinsert ignore into journalissuearticles values(\epsilon_i > k);$ 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