On the choice of statistical model for one-dimensional P-algorithms

Algorithms based on statistical models compete favorably with other global optimization algorithms as proved by extensive testing results. Recently, techniques were developed for theoretically estimating the rate of convergence of global optimization algorithms with respect to the underlying statistical models. In the present paper these techniques are extended for theoretical investigation of P-algorithms without respect to a statistical model. Theoretical estimates may eliminate the need for lengthy experimental investigation which previously was the only method for comparison of the algorithms. The results obtained give new insight into the role of the underlying statistical model with respect to the asymptotic properties of the algorithm which will be useful for the implementation of new versions of the algorithms.