Some Methods of Detection of Outliers in Linear Regression Model

An outlier is an observation that deviates markedly from the majority of the data. To know which observation has greater influence on parameter estimate, detection of outlier is very important. There are several methods for detection of outliers available in the literature. A good number of test-statistics for detecting outliers have been developed. In contrast to detection, outliers are also tackled through robust regression techniques like, M-estimator, Least Median of Square (LMS). Robust regression provides parameter estimates that are insensitive to the presence of outliers and also helps to detect outlying observations. Recently, Forward Search (FS) method has been developed, in which a small number of observations robustly chosen are used to fit a model through Least Square (LS) method. Then more number of observations are included in the subsequent steps. This forward search procedure provides a wealth of information not only for outlier detection but, much more importantly, on the effect of each observation on aspects of inferences about the model. It also reveals the masking problem, if present, very nicely in the data.