The resampling approach application to complex systems reliability analysis and forecasting

Estimation of function expectation θ = Ef(X1, X2, ..., Xm) is considered. For independent variables X1, X2, ..., Xm, sample populations H1, H2, ...,Hm are available as the primary data. The resampling approach uses the usual simulation procedure. For that, the random variables {Xi} are not generated by random number generators in accordance with the estimated probabilistic distributions, but are extracted from the present samples at random. In the presented paper some theoretical results of the author for the case of small samples will be reviewed. Ones concern the hierarchical resampling, the controlled resampling, the interval estimation, the case of a dependent observations etc.