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On likelihood distance for outliers detection

W Wang1, S C Chow, W W Wei

  • 1Department of Statistics, Temple University, Philadelphia, Pennsylvania 19122, USA.

Journal of Biopharmaceutical Statistics
|November 1, 1995
PubMed
Summary
This summary is machine-generated.

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The likelihood distance is commonly used for outlier detection. This study demonstrates that its comparison to a chi-squared distribution is inappropriate, as it does not follow this distribution for large samples.

Area of Science:

  • Statistics
  • Data Analysis

Background:

  • The likelihood distance is a standard metric for identifying outlying observations in statistical analysis.
  • Previous research suggested comparing the likelihood distance to a chi-squared distribution for large sample sizes.

Purpose of the Study:

  • To investigate the asymptotic behavior of the likelihood distance.
  • To determine the appropriate distribution for the likelihood distance in large samples.
  • To correct the methodology for outlier detection using likelihood distance.

Main Methods:

  • Asymptotic analysis of the likelihood distance statistic.
  • Theoretical derivation of the limiting distribution.

Main Results:

  • The likelihood distance does not asymptotically follow a chi-squared distribution.

Related Experiment Videos

  • The likelihood distance converges to 0 in probability as sample size increases.
  • A sample size-dependent multiplication factor is required for a nondegenerate limiting distribution.

    • Conclusions:

    • The use of a chi-squared distribution for likelihood distance is inappropriate for large samples.
    • A modified statistic with a sample size factor is necessary for accurate outlier detection.
    • The limiting distribution of the modified statistic is dependent on the specific statistical model.