Prescriptions for Working Statisticians pp 120-147 | Cite as

# Identification of Outliers

## Abstract

One of the most vexing of problems in data analysis is the determination of whether or not to discard some observations because they are inconsistent with the rest of the observations and/or the probability distribution assumed to be the underlying distribution of the data. One direction of research activity related to this problem is that of the study of robust statistical procedures (cf. Huber [1981]), primarily procedures for estimating population parameters which are insensitive to the effect of “outliers”, i.e., observations inconsistent with the assumed model of the random process generating the observations. Typically, the robust procedure involves some “trimming” or down-weighting procedure, wherein some fraction of the extreme observations are automatically eliminated or given less weight to guard against the potential effect of outliers.

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### References

- Barnett, V. and Lewis, T., 1978.
*Outliers in Statistical Data*. New York: Wiley.MATHGoogle Scholar - Beckman, R. J. and Cook, R. D. 1983. Outlier……….s.
*Technometrics***25**(May): 119–49.MathSciNetMATHCrossRefGoogle Scholar - Belsley, D. A., Kuh, E., and Welsch, R. E. 1980.
*Regression Diagnostics*. New York: Wiley.MATHCrossRefGoogle Scholar - Cook, R. D. 1977. Detection of influential observations in linear regression.
*Technometrics***19**(February): 15–18.MathSciNetMATHCrossRefGoogle Scholar - Cook, R. D. 1979. Influential observations in linear regression.
*Journal of the American Statistical Association***74**(March): 169–74.MathSciNetMATHCrossRefGoogle Scholar - Cook, R. D. and Weisberg, S. 1982.
*Residuals and Influence in Regression*. New York: Chapman and Hall.MATHGoogle Scholar - Ferguson, T. S. 1961a. On the rejection of outliers. In
*Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability*, Vol. 1, ed. J. Neyman. Berkeley: University of California Press, pp. 253–87.Google Scholar - Ferguson, T. S. 1961b. Rules for rejection of outliers.
*Revue de l’Institut International de Statistique***29**(No. 3): 29–43.MathSciNetMATHCrossRefGoogle Scholar - Grubbs, F. E. 1950. Sample criteria for testing outlying observations.
*Annals of Mathematical Statistics***21**(March): 27–58.MathSciNetMATHCrossRefGoogle Scholar - Hawkins, D. M. 1978. Fractiles of an extended multiple outlier test.
*Journal of Statistical Computation and Simulation***8**: 227–36.CrossRefGoogle Scholar - Hawkins, D. M. 1980.
*Identification of Outliers*. New York: Chapman and Hall.MATHGoogle Scholar - Huber, P. 1981.
*Robust Statistics*. New York: Wiley.MATHCrossRefGoogle Scholar - Karlin, S. and Truax, D. R. 1960. Slippage problems.
*Annals of Mathematical Statistics***31**(June): 296–324.MathSciNetMATHCrossRefGoogle Scholar - Kudo, A. 1956. On the testing of outlying observations.
*Sankhya***17**(June): 67–76.MathSciNetMATHGoogle Scholar - Murphy, R. B. 1951.
*On Tests for Outlying Observations*. Ph. D. thesis, Princeton University. Ann Arbor: University Microfilms.Google Scholar - Pearson, E. S. and Chandra Sekar, C. 1936. The efficiency of statistical tools and a criterion for the rejection of outlying observations.
*Biometrika***28**: 308–20.MATHGoogle Scholar - Pearson, E. S. and Stephens, M. A. 1964. The ratio of range to standard deviation in the same normal sample.
*Biometrika***51**: 484–87.MathSciNetMATHGoogle Scholar - Rosner, B. 1975. On the detection of many outliers.
*Technometrics***17**(May): 221–27.MathSciNetMATHCrossRefGoogle Scholar - Rosner, B. 1983. Percentage points for a generalized ESD many-outlier procedure.
*Technometrics***25**(May): 165–72.MATHCrossRefGoogle Scholar - Thompson, W. R. 1935. On a criterion for the rejection of observations and the distributions of the ratio of the deviation to the sample standard deviation.
*Annals of Mathematical Statistics***6**: 214–19.MATHCrossRefGoogle Scholar - Tietjen, G. L. and Moore, R. M. 1972. Some Grubbs-type statistics for the detection of several outliers.
*Technometrics***14**(August): 583–97.CrossRefGoogle Scholar - Walsh, J. E. 1950. Some nonparametric tests of whether the largest observations of a set are too large or too small.
*Annals of Mathematical Statistics***21**(December): 583–92.MathSciNetMATHCrossRefGoogle Scholar - (see also correction 1953
*Annals of Mathematical Statistics***24**(March): 134–35).CrossRefGoogle Scholar - Walsh, J. E. 1958. Large sample nonparametric rejection of outlying observations.
*Annals of the Institute of Statistical Mathematics***10**: 223–32.CrossRefGoogle Scholar - Weisberg, S. 1980.
*Applied Linear Regression*. New York: Wiley.MATHGoogle Scholar