Subsampling continuous parameter random fields and a Bernstein inequality

Abstract

In the present paper we study the subsampling methodology for approximating the distribution of statistics estimating some unknown parameter associated with the probability distribution of a continuous parameter random field. We first obtain a new Bernstein-type inequality for dependent processes connected with strong mixing coefficients. With the help of the new inequality, we prove that subsampling continuous parameter random fields works under minimal weak dependence assumptions, and relax the (already quite weak) mixing condition that was imposed by Politis and Romano (1994) in order to show the validity of subsampling for discrete parameter random fields.