Outlier Detection Method in Linear Regression Based on Sum of Arithmetic Progression

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.