MINIMUM DISTANCE METHODS BASED ON QUADRATIC DISTANCES FOR TRANSFORMS IN SIMPLE LINEAR-REGRESSION MODELS

Minimum distance estimators and test statistics based on quadratic distances for transforms are introduced in simple linear regression models. Asymptotic properties of quadratic distance estimators and tests for the error distributions are derived. The modified quadratic distance estimator is shown to be efficient provided that the error distribution is symmetric and the derivative of the logarithm of the error density is a linear combination of the transforms.