Eficiency of Ordinary Least Squares Estimators from Trimmed and Winsorized Samples in Linear Regression

Abstract

The problem of estimating the parameters of the simple linear regression model when the samples are symmetrically trimmed or Winsorized is considered. The efficiency of the ordinary least squares estimators (OLSE) relative to the best linear unbiased estimators (O-BLUE) from trimmed, Winsorized and complete samples is discussed. The exact relative efficiencies are given for some symmetric distributions and for values of 5 ≤ n ≤ 20. It is found that the (OLSE) estimators based on trimmed data are almost as efficient as the (O-BLUE) estimators for a variety of distributional specifications, while Winsorizing performs rather less well in several cases and marginally better in a few. It is found that for the standard normal and the scale contaminated normal distributions, the (OLSE) from trimmed samples maintain very high efficiencies relative to the (O-BLUE). Similarly, for the Winsorized (OLSE). But as the tails of the distribution become heavier—e.g. the double exponential distribution—the loss in efficiency of the Winsorized estimators becomes larger. The trimmed (OLSE) were better for heavier-tailed distributions than the Winsorized.

KEY WORDS:

• Linear Regression
• Trimmed
• Winsorized
• O-BLUE
• OLSE
• Efficiency
• Symmetric Distributions