Outlier Detection Under Star-Contoured Errors

Abstract

Consider as Gaussian observations with common mean μ and dispersion matrix Σ. Approaches for detecting outlying observations include the R–Student statistics in regression diagnostics, as well as tests due to Grubbs, Dixon, and Ferguson using order statistics. All are known to be valid under Σ ; Grubbs’s test also holds under an equicorrelated matrix Σ(ρ) and the more general structure Σ . Dispersion mixtures of Gaussian errors having Σ(ρ) and Σ() are studied in detail; their densities have star-shaped contours as encountered on occasion in practice. Under these mixtures, the aforementioned diagnostics all are shown to be exact in significance level and in power as for the case where Σ . This expands considerably their range of applicability in practice. Case studies serve to illustrate essentials of the findings.

AMS Subject Classification:

• 62E10
• 62F04

Keywords:

• Outlying data
• Deletion diagnostics
• Order statistics
• Structured errors