title: Outlier detection method in linear regression based on sum of arithmetic progression.
abstract: We introduce a new nonparametric outlier detection method for linear series, which requires no missing or removed data imputation. For an arithmetic progression (a series without outliers) with n elements, the ratio (R) of the sum of the minimum and the maximum elements and the sum of all elements is always 2/n : (0,1]. R ≠ 2/n always implies the existence of outliers. Usually, R < 2/n implies that the minimum is an outlier, and R > 2/n implies that the maximum is an outlier. Based upon this, we derived a new method for identifying significant and nonsignificant outliers, separately. Two different techniques were used to manage missing data and removed outliers: (1) recalculate the terms after (or before) the removed or missing element while maintaining the initial angle in relation to a certain point or (2) transform data into a constant value, which is not affected by missing or removed elements. With a reference element, which was not an outlier, the method detected all outliers from data sets with 6 to 1000 elements containing 50% outliers which deviated by a factor of ±1.0e - 2 to ±1.0e + 2 from the correct value.
authors.affiliation: Group Bio-Process Analysis Technology, Technische Universität München, Weihenstephaner Steig 20, 85354 Freising, Germany ; Institut für Landtechnik und Tierhaltung, Vöttinger Straße 36, 85354 Freising, Germany ; Computer Unit, Faculty of Agriculture, University of Ruhuna, Mapalana, 81100 Kamburupitiya, Sri Lanka.
authors.forename: K K L B
authors.initials: KK
authors.lastname: Adikaram
authors.affiliation: Group Bio-Process Analysis Technology, Technische Universität München, Weihenstephaner Steig 20, 85354 Freising, Germany.
authors.forename: M A
authors.initials: MA
authors.lastname: Hussein
authors.affiliation: Institut für Landtechnik und Tierhaltung, Vöttinger Straße 36, 85354 Freising, Germany.
authors.forename: M
authors.initials: M
authors.lastname: Effenberger
authors.affiliation: Group Bio-Process Analysis Technology, Technische Universität München, Weihenstephaner Steig 20, 85354 Freising, Germany.
authors.forename: T
authors.initials: T
authors.lastname: Becker
mesh_terms: D003627:Data Interpretation, Statistical; D016014:Linear Models; D055641:Mathematical Concepts; D009716:Numerical Analysis, Computer-Assisted