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

Algorithms based on statistical models compete favourably with other global optimisation algorithms as proven by the extensive testing results. Recently, techniques have been developed for theoretical estimation of the rate of convergence of global optimisation algorithms with respect to the underlying statistical models. In this paper such 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 has been previously the only method for comparing 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 implementation of new versions of algorithms.