Breakdown theory for bootstrap quantiles

Breakdown point theory for implied probability bootstrap

This paper studies robustness of bootstrap inference methods under moment conditions. In particular, we compare the uniform weight and implied probability bootstraps by analyzing behaviors of the bootstrap quantiles when an outlier takes an arbitrarily large value, and derive the breakdown points for those bootstrap quantiles. The breakdown properties characterize the situation where the implie...

Bahadur representations for bootstrap quantiles 1

BREAKDOWN POINT THEORY FOR IMPLIED PROBABILITY BOOTSTRAP By

This paper studies robustness of bootstrap inference methods under moment conditions. In particular, we compare the uniform weight and implied probability bootstraps by analyzing behaviors of the bootstrap quantiles when outliers take arbitrarily large values, and derive the breakdown points for those bootstrap quantiles. The breakdown point properties characterize the situation where the impli...

Iterated Smoothed Bootstrap Confidence Intervals for Population Quantiles

This paper investigates the effects of smoothed bootstrap iterations on coverage probabilities of smoothed bootstrap and bootstrap-t confidence intervals for population quantiles, and establishes the optimal kernel bandwidths at various stages of the smoothing procedures. The conventional smoothed bootstrap and bootstrap-t methods have been known to yield one-sided coverage errors of orders O(n...

VARIANCE ESTIMATION FOR SAMPLE QUANTILES USING THE m OUT OF n BOOTSTRAP

i . Introduction Suppose that X1,. 9 9 Xn constitute a random sample of size n taken from a distribution F. Let X(j) denote the j th smallest datum in the sample. For a fixed p E (0, 1), assume that F has a continuous and positive density f on F -1 (O) for an open neighbourhood O containing p. Denote by ~p = F-l(p) the unique p-th quantile of F . The p-th sample quantile X(r) is a natural and c...