(Received August 24, 1989; revised February 22, 1990)
Abstract. In this paper we consider the sampling properties of the bootstrap process, that is, the empirical process obtained from a random sample of size n (with replacement) of a fixed sample of size n of a continuous distribution. The cumulants of the bootstrap process are given up to the order n-1 and their unbiased estimation is discussed. Furthermore, it is shown that the bootstrap process has an asymptotic minimax property for some class of distributions up to the order n-1/2.
Key words and phrases: Bootstrap process, cumulants, unbiased estimators, asymptotic minimax property.