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Bootstrap for nonparametric regression has been around for more than 30 years. Nevertheless, most results are based on assuming an additive regression model with respect to independent and identical (i.i.d.) errors. An exception is the Local Bootstrap of Shi [23] for which, however, no bootstrap consistency results are available. We attempt to remedy this here while at the same time showing bootstrap consistency for a more general class of methods that fall under the heading of Model-free Bootstrap of Politis [18].

Asymptotic validity of bootstrap confidence intervals in nonparametric regression without an additive model