title: On likelihood distance for outliers detection.
abstract: The likelihood distance has been widely used to detect outlying observations in data analysis. Cook and Weisberg (5) suggested that the likelihood distance may be compared to a chi 2 distribution for large samples. In this paper, we show that use of the chi 2 distribution is inappropriate. The results indicate that the likelihood distance does not follow an asymptotically chi 2 distribution. Instead, it converges to 0 in probability as the sample size increases. We show that for a nondegenerate limiting distribution, a multiplication factor related to the sample size n is needed. In general, the limiting distribution of this modified statistic is model-dependent.
authors.affiliation: Department of Statistics, Temple University, Philadelphia, Pennsylvania 19122, USA.
authors.forename: W
authors.initials: W
authors.lastname: Wang
authors.forename: S C
authors.initials: SC
authors.lastname: Chow
authors.forename: W W
authors.initials: WW
authors.lastname: Wei
mesh_terms: D003627:Data Interpretation, Statistical; D006801:Humans; D016013:Likelihood Functions; D016014:Linear Models; D012044:Regression Analysis; D012107:Research Design; D012494:Sampling Studies