Noncentral Limit Theorem and the Bootstrap for Quantiles of Dependent Data

Details Noncentral Limit Theorem and the Bootstrap for Quantiles of Dependent Data Noncentral Limit Theorem and the Bootstrap for Quantiles of Dependent Data

2012-04-25

arxiv.org/abs/1204.5633v1

Mathematics

Statistics Theory

Scientific paper

We will show under minimal conditions on differentiability and dependence
that the central limit theorem for quantiles holds and that the block bootstrap
is weakly consistent. Under slightly stronger conditions, the bootstrap is
strongly consistent. Without the differentiability condition, quantiles might
have a non-normal asymptotic distribution and the bootstrap might fail.

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