APPROXIMATE POWER FUNCTIONS FOR SOME ROBUST TESTS OF REGRESSION COEFFICIENTS Thomas J . Rothenberg Department o f Economics U n i v e r s i t y o f C a l i f o r n i a , Berkeley Research Papers i n Economics No. 84-1 Summary Edgeworth expansions are developed f o r the d i s t r i b u t i o n functions o f some t e s t s t a t i s t i c s i n the normal l i n e a r regression model where the e r r o r covariance matrix i s unknown. Tests based on generalized l e a s t squares estimates and also on ordinary l e a s t squares estimates are considered. In both cases, adjustments t o the asymptotic c r i t i c a l The approxi values are found and approximate l o c a l power c a l c u l a t e d . and a u t o c o r r e l a t i o n . mations are applied to a number o f examples, i n c l u d i n g h e t e r o s c e d a s t i c i t y