SUMMARY: Consider the usual linear regression model y = Xß +ε, where the vector ε has E(ε) = 0, cov (ε) = σ2 V, where V is known. Let e = y-ŷ be the least squares residual vector. It is shown that a test based on the transformed residual vector d* = V-1 e has, in the class of linear transformations of e, certain optimal power properties for detecting the presence of a single outlier when the label of the outlier observation is unknown. The outlier model considered here is that of shift in location.
- Linear regression
ASJC Scopus subject areas
- Statistics and Probability
- Agricultural and Biological Sciences (miscellaneous)
- Agricultural and Biological Sciences(all)
- Statistics, Probability and Uncertainty
- Applied Mathematics