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.
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