On likelihood distance for outliers detection
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Updated: Nov 2, 2026

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
Published on: March 1, 2022
1Department of Statistics, Temple University, Philadelphia, Pennsylvania 19122, USA.
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.
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