For the detection of outliers (observations which are seemingly different from the others) the method of testing hypotheses is most often used. This approach, however, depends on the level of significance adopted by the investigator. Moreover, it can lead to the undesirable effect of “masking” of the outliers. This paper presents an alternative method of outlier detection based on the Akaike information criterion. The theory presented is applied to analysis of the results of beet leaf mass determination.
@article{bwmeta1.element.doi-10_2478_bile-2013-0022,
author = {Andrzej Kornacki},
title = {Detection of outlying observations using the Akaike information criterion},
journal = {Biometrical Letters},
volume = {50},
year = {2013},
pages = {117-126},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_bile-2013-0022}
}
Andrzej Kornacki. Detection of outlying observations using the Akaike information criterion. Biometrical Letters, Tome 50 (2013) pp. 117-126. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_bile-2013-0022/
Akaike H. (1973): Information theory and an extension of the maximum likelihood principle. 2nd International Symposium on Information Theory, eds. B.N. Petrv and F. Csaki, Budapest; Akademiai Kiado: 267-281. | Zbl 0283.62006
Akaike H. (1977): On entropy maximization principle. Proc Symposium on Applications of Statistics, ed. P.R. Krishnaiah, Amsterdam: North Holland: 27-47. Barnett V., Lewis T. (1993): Outliers in Statistical Data. John Wiley & Sons.
Breuning M., Kriegel H.P, Sander J. (2000): LOF: Identifying Density-Based Local Outliers. In: Proceedings of the ACM SIGMOND Conference: 93-104.
David H.A. (1979): Pariadkowyje statistiki. Mockba Nauka.
Dzida K., Jarosz Z., Michalojć Z. (2011): The effect of diversified potassium fertilization on the field and chemical composition on Beta Vulgaris L. Acta Sci. Pol. Hortus. Cultus 10(40): 263-274.
Ellenberg J.H. (1976): Testing for a single outlier from a general linear regression. Biometrics 32: 637-645.[PubMed][Crossref] | Zbl 0338.62039
Ferguson T.S. (1961): On the rejection of outliers. In Proc. Fourth Berkeley Symposium Math. Statist. Prob.1: 253-287. | Zbl 0129.32702
Galpin J.S., Hawkins D.M. (1981): Rejection of a single outlier in two or three-way layouts. Technometrics 23: 65-70. | Zbl 0465.62070
Grubbs F.E. (1950): Sample criteria for testing outlying observations. Ann. Math. Statist. 21: 27-58. | Zbl 0036.21003
Grubbs F.E. (1969): Procedures for detecting outlying observations in samples. Technometrics 11: 1-21.[Crossref]
Joshi P.C. (1972): Some slippage tests of mean for a single outlier in linear regression. Biometrika 59: 109-120.[Crossref] | Zbl 0234.62028
Karlin S., Traux D. (1960): Slippage problems. Ann. Math. Statist 31: 296-324.[Crossref] | Zbl 0131.35602
Pan J.X., Fang K.T. (1995): Multiple outlier detection in growth curve model with unstructured covariance matrix. Ann. Inst. Statist. Math. 47: 137-153. | Zbl 0822.62045
Ramaswamy S., Rastogi R., Shim K. (2000): Efficient algorithms for mining outliers from large data sets. In: Proceedings of the ACM SIGMOND Conference on Management of data. Dallas: 427-438.
Rosseuw P., Leroy A. (2000): Robust Regression and Outlier Detection. John Wiley & Sons.
Sakamoto Y., Ishigura M. (1986): Akaike Information Criterion Statistics. Tokyo Reidel Publishing Company.
Schwager S.J., Margolin B.H. (1982): Detection of multivariate normal outliers. Ann. Statist. 10: 943-954. | Zbl 0497.62046
Srivastava M.S., Von Rosen D. (1998): Outliers in Multivariate Regression Models. J. Mult. Anal. 65: 195-208. | Zbl 1127.62376
Stefansky W. (1972): Rejecting outliers in factorial designs. Technometrics 14: 469-479 [Crossref] | Zbl 0284.62053
Tietjen G.L., Moore R.H. (1972): Some Grubbs-type statistics for the detection of several outliers. Technometrics 14: 583-597.[Crossref]
Wilks S.S. (1963): Multivariate statistical outliers. Sankhya A. 25: 406-427. | Zbl 0128.13401