Jolliffe I. Principal Component Analysis (2ed., Springer, 2002)(518s)

10Outlier Detection, InfluentialObservations, Stability, Sensitivity,and Robust Estimation of PrincipalComponentsThis chapter deals with four related topics, which are all concerned withsituations where some of the observations may, in some way, be atypical ofthe bulk of the data.First, we discuss the problem of detecting outliers in a set of data. Outliersare generally viewed as observations that are a long way from, orinconsistent with, the remainder of the data. Such observations can, butneed not, have a drastic and disproportionate effect on the results of variousanalyses of a data set. Numerous methods have been suggested fordetecting outliers (see, for example, Barnett and Lewis, 1994; Hawkins,1980); some of the methods use PCs, and these methods are described inSection 10.1.The techniques described in Section 10.1 are useful regardless of the typeof statistical analysis to be performed, but in Sections 10.2–10.4 we lookspecifically at the case where a PCA is being done. Depending on theirposition, outlying observations may or may not have a large effect on theresults of the analysis. It is of interest to determine which observations doindeed have a large effect. Such observations are called influential observationsand are discussed in Section 10.2. Leaving out an observation is onetype of perturbation to a data set. Sensitivity and stability of PCA withrespect to other types of perturbation is the subject of Section 10.3.Given that certain observations are outliers or influential, it may bedesirable to adapt the analysis to remove or diminish the effects of suchobservations; that is, the analysis is made robust. Robust analyses havebeen developed in many branches of statistics (see, for example, Huber(1981); Hampel et al. (1986) for some of the theoretical background, and