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) withnelements, the ratio (R) of the sum of the minimum and the maximum elements and the sum of all elements is always2/n:(0,1].R≠2/nalways implies the existence of outliers. Usually,R<2/nimplies that the minimum is an outlier, andR>2/nimplies 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-2to±1.0e+2from the correct value.