Abstract
For testingk upper or lower outliers in a normal sample, the sampling distribution of the likelihood-ratio statistic is still unknown in the literature except fork=1. In this paper, we find its exact distribution fork=2 and tabulate the extensive critical values, which are compared with the traditional simulated values.
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References
Barnett, V. andLewis, T. (1994).Outliers in Statistical Data. John Wiley & Sons Chichester, 3rd ed.
Fisher, R. A. (1929). Tests of significance in harmonic analysis.Proceedings of the Royal Statistical Society, 125:54–59.
Grubbs, F. E. (1950). Sample criteria for testing outlying observations.The Annals of Mathematical Statistics, 21:27–58.
Grubbs, F. E. (1969). Procedures for detecting outlying observations in samples.Technometrics, 11:1–21.
Grubbs, F. E. andBeck, G. (1972). Extension of sample sizes and percentage points for significance tests of outlying observations.Technometrics, 14:847–856.
Kimber, A. C. andStevens, H. J. (1981). The null distribution of a test for two upper outliers in an exponential sample.Applied Statistics, 30:153–157.
Zhang, J. (1998). Tests for multiple upper or lower outliers in an exponential sample.Journal of Applied Statistics, 25:245–255.
Zhang, J. andWang, X. (1998). Unmasking test for multiple upper or lower outliers in normal samples.Journal of Applied Statistics, 25:257–261.
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The research is partially supported by the National Sciences and Engineering Research Council of Canada.
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Zhang, J., Yu, K. The null distribution of the likelihood-ratio test for one or two outliers in a normal sample. TEST 15, 141–150 (2006). https://doi.org/10.1007/BF02595422
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DOI: https://doi.org/10.1007/BF02595422