Heuristic proof of the formula for the asymptotic deficiency in the case of regression model
In the present paper, following [1], [2], we heuristically obtain a formula (see (3.16)) for the limit of the difference between the power of the asymptotically optimal test and the power of the asymptotically most powerful test based on the stochastic expansion of the logarithm of the likelihood ratio in the regression model. It is demonstrated that this difference tends to zero with arbitrary rate due to behavior of regression coefficients in contrast to regular cases for which this order equals n-1.