Seeking outlying subsets under star-contoured errors

ABSTRACT

Given observations with dispersion matrix , a pervading issue is whether shifts have occurred in designated subsets of the observations. Early work on single shifts used order statistics or the R–Student statistics as diagnostics, initially derived under i.i.d. Gaussian assumptions. These diagnostics recently have been shown to remain exact in level and power under equicorrelation and more general dispersion structures, and under star-contoured mixtures supplanting Gaussian errors, with an accounting for irregularities engendered by shifts at other than the designated cases. Extensions here pertain to outlying subsets using the -Fisher diagnostics showing invariance of its distribution and of related diagnostics under more general dispersion structures and mixtures over these. Shifts occurring at cases other than those designated induce doubly noncentral distributions. These elicit profound disturbances in operating characteristics of the diagnostics, serving in turn to explain masking and swamping, and the discovery of hidden “regression effects” among outliers. Evidence for anomalies arising from denominator noncentralities rests on two-sided rejection rules to be given. Numerical studies serve to illuminate the essence of the findings in practice.

KEYWORDS:

• Outlying subsets
• structured errors
• mixtures
• invariance
• misdirected inferences

AMS SUBJECT CLASSIFICATION:

• 62E10
• 62F04