The Cross-Entropy Method for Estimation

D. P. Kroese, R. Y. Rubinstein, and P. W. Glynn

To appear in Handbook of Statistics, Vol. 31, Eds. V. Govindaraju and C. R. Rao, Elsevier

This chapter describes how difficult statistical estimation problems can often be solved efficiently by means of the cross-entropy (CE) method. The CE method can be viewed as an adaptive importance sampling procedure that uses the cross-entropy or Kullback–Leibler divergence as a measure of closeness between two sampling distributions. The CE method is particularly useful for the estimation of rare-event probabilities. The method can also be used to solve a diverse range of optimization problems. The optimization setting is described in detail in the chapter entitled “The Cross-Entropy Method for Optimization”.