APPROXIMATE MAXIMUM LIKELIHOOD ESTIMATION IN LINEAR REGRESSION

MICHAEL A. MAGDALINOS

Department of Statistics and Information Science, The Athens University of Economics and Business, 76, Patission Street, Athens 104 34, Greece

(Received March 3, 1989; revised October 25, 1991)

Abstract. The application of the ML method in linear regression requires a parametric form for the error density. When this is not available, the density may be parameterized by its cumulants (κ_{i}) and the ML then applied. Results are obtained when the standardized cumulants (γ_{i}) satisfy γ_{i} = κ_{i+2}/κ_{2}^{(i+2)/2} = O(v^{i}) as v → 0 for i > 0.

Key words and phrases: Regression, maximum likelihood, non-normal errors, Edgeworth approximation.