Pitman Closeness Comparison of Least Squares and Stein-Rule Estimators in Linear Regression Models with Non-Normal Disturbances

SYNOPTIC ABSTRACT

Employing large sample asymptotic theory, an asymptotic approximation for the Pitman closeness probability is derived and a comparison of the least squares and Stein-rule estimators is made when the aim is to estimate the coefficients in a linear regression model. Since the disturbances are assumed to be not necessarily normal, the Edgeworth expansion is utilized to obtain an approximation for the characteristic function from the cumulant generating function.

Key Words and Phrases:

• asymptotic approximation
• non-normal
• Pitman closeness
• regression
• Stein-rule