Geometric consistency for regression model estimation and testing in climatology and meteorology

Abstract

The effects of outliers on linear regression are examined. The sensitivity of classical least‐squares (LS) procedures to outliers is shown to be associated with the geometric inconsistency between the data space and the analysis space. This is illustrated for both estimation and inference. A geometrically consistent procedure based on the Euclidean distance is proposed. This procedure involves the least absolute deviation (LAD) regression and a new permutation test for matched pairs (PTMP). Comparisons made with LS techniques demonstrate that the proposed procedure is more resistant to the existence of outliers in the data set and leads to more intuitive results. Applications and illustrations using meteorological and climatological data are also discussed.