The local bootstrap for kernel estimators under general dependence conditions

摘要: We consider the problem of estimating distribution a nonparametric (kernel) estimator conditional expectation g(x; φ) = E(φ(X t+1) | Y t,m x) strictly stationary stochastic process {X t , t ≥ 1}. In this notation φ(·) is real-valued Borel function and segment lagged values, i.e., Yt,m=(Xt-i 1,Xt-i 2,...,Xt-i m), where integers i i satisfy 0 ≤ i1 . show that under fairly weak set conditions on 1}, an appropriately designed simple bootstrap procedure correctly imitates X t+1 given selective past approximates class estimators considered. The proposed entirely nonparametric, its main dependence assumption refers to strongly mixing with polynomial decrease rate it not based any particular assumptions model structure generating observations.