Analysis of Outliers with Adjusted Residuals

Many statistical procedures designed to guard against the occurrence of outliers or spurious observations in normal theory are based upon examining the magnitude of the residuals. A major difficulty involved is caused by the fact that the residuals are correlated. It is shown that one way to avoid such difficulty is to adjust the residuals using information from an auxiliary experiment so that the adjusted residuals become uncorrelated. For the problem of making inferences about the unknown mean of a normal population N(μ, σ2) with known σ2, this leads to a set of estimation procedures by which the observation(s) associated with the largest adjusted residual(s) in magnitude will be excluded. Certain properties of the procedures are discussed and exact numerical results are given for the cases of one and two spurious observations. Generalization to the case of unknown variance and to the general linear model is also given.