Subsampling with Unknown Convergence Rate

Abstract

Let X₁,…, X _n be an observed stretch of a (strictly) stationary, strong mixing sequence of random variables X_t, t ∈ Z} taking values in an arbitrary sample space S; the probability measure generating the observations is denoted by P. The strong mixing condition means that the sequence tends to zero as k tends to infinity, where A and B are events in the σ-algebras generated by X_t, t < 0} and X_t, t ≥ k}, respectively; the case where X₁,…,X _n are independent, identically distributed (i.i.d.) is an important special case of the general scenario.