On the Behavior of Some Estimators from Probability Plots

Abstract

Probability plots are popular graphical methods used to assess distributional assumptions. Under a location-scale model, the plot tends to lie on a straight line. A common practice in this situation is to fit a line through the plot and use the intercept and slope of the fitted line as estimates of the location and scale parameters. What are the properties of these estimators? Estimators from weighted least squares lines are considered, and their asymptotic, finite-sample, robustness, and optimality properties are discussed. Included among these are the ordinary least squares estimators and estimators from least squares lines fitted after trimming or Winsorizing some of the extreme order statistics.

Key Words:

• Asymptotic distribution
• Graphical methods
• Least squares
• L estimators
• Location scale
• Robustness