Care and Handling of Univariate Outliers in the General Linear Model to Detect Spuriosity- A

We deal with the situation covered by the univariate general linear model, that is, it is intended that n observations be generated in accordance with the usual model y = Xβ + e however, it is feared that k of the observations are spurious, that is, not generated in the manner intended, so that for an unknown set of k distinct integers, say (i 1, … ik ), a subset of the first n integers, we have, specifically, that ytj , = x tj ′, β + a j , + ∊ tj , where in general x t ′ denotes the t-th row of X, and where (a 1, …, a k ), so called shift parameters, are such that – ∞ < a j , < ∞. In this paper, we discuss the posterior distribution of β, when indeed it is assumed a priori that any given set of k observations has uniform probability I/( n k ) of being spurious. The properties of the posterior of β are discussed, and the results used in an example using data generated from a response surface design. Ad hoc procedures are discussed for gaining information on k, when k is unknown. These ad hoc procedures ar...