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Abstract:
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In "Qualms about bootstrap confidence intervals," Schenker (1985) showed by example that the BC bootstrap breaks down for practical sample sizes. Efron devised the BCa method in "Better bootstrap confidence intervals," Efron (1987) to overcome the problem. We revisit the issues by estimating variances in a nonparametric setting. We show through simulation that even for a sample size n>=200 for certain heavy-tailed and skewed distributions, the convergence of the second order accurate bootstrap methods BCa, ABC, and tilted bootstrap is slow and all of the methods provide true confidence levels that are at least 5% below their advertised confidence levels. We illustrate this at confidence levels of 50%, 75% and 90%. For sample sizes n>=1000 to adequately show the proper pattern of convergence, we need the standard deviation of the Monte Carlo approximation of the proportion to be 0.005.
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