Large deviations for bootstrapped empirical measures (Q470054)

The authors are concerned with large deviation principles (LDPs) with good rate functions for weighted bootstrap sequences computed from triangular arrays of observable random variables taking their values in a Polish space. Two main theorems establish LDPs and rate functions for the conditional case (observations are taken as fixed) and the unconditional case (both the weights and the observations are considered as random) in weak convergence topology, provided that an LDP for the weights (in Wasserstein distance) is at hand. Also, representation results for the rate functions are derived.NEWLINENEWLINEApplications comprise large deviations properties of Efron's bootstrap, the ``\(m\) out of \(n\)'' bootstrap, the i.i.d.\ weighted bootstrap, the multivariate hypergeometric bootstrap, a bootstrap procedure generated from deterministic weights, and certain block bootstrap methods. In this, proofs concerning the necessary LDPs for the weights are deferred to a supplementary article.