Computation of an exact confidence set for a maximum point of a univariate polynomial function in a given interval

Construction of a confidence set for a maximum point of a function is an important statistical problem. Wan et al. (2015) provided an exact 1−α confidence set for a maximum point of a univariate polynomial function in a given interval. In this paper, we give an efficient computational method for computing the confidence set of Wan et al. (2015). We demonstrate with two examples that the new method is substantially more efficient than the proposals by Wan et al. (2015). Matlab programs have been written which make the implementation of the new method straightforward.