A Note on Conditional Versus Joint Unconditional Weak Convergence in Bootstrap Consistency Results

  title={A Note on Conditional Versus Joint Unconditional Weak Convergence in Bootstrap Consistency Results},
  author={Axel B{\"u}cher and Ivan Kojadinovic},
  journal={Journal of Theoretical Probability},
The consistency of a bootstrap or resampling scheme is classically validated by weak convergence of conditional laws. However, when working with stochastic processes in the space of bounded functions and their weak convergence in the Hoffmann–Jørgensen sense, an obstacle occurs: due to possible non-measurability, neither laws nor conditional laws are well defined. Starting from an equivalent formulation of weak convergence based on the bounded Lipschitz metric, a classical circumvention is to… 

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