WEIGHTED AVERAGE POWER SIMILAR TESTS FOR STRUCTURAL CHANGE IN THE GAUSSIAN LINEAR REGRESSION MODEL

Average exponential F tests for structural change in a Gaussian linear regression model and modifications thereof maximize a weighted average power that incorporates specific weighting functions to make the resulting test statistics simple+ Generalizations of these tests involve the numerical evaluation of ~potentially! complicated integrals+ In this paper, we suggest a uniform Laplace approximation to evaluate weighted average power test statistics for which a simple closed form does not exist+ We also show that a modification of the avg-F test is optimal under a very large class of weighting functions and can be written as a ratio of quadratic forms so that both its p-values and critical values are easy to calculate using numerical algorithms+