A queueing analyst is handed a random sample of 75 customer waiting times from a call-center. Exploratory plots reveal a long right tail and substantial positive skew. She must deliver a 95 % confidence interval for the population median but wishes to avoid making any distributional assumptions and wants the interval endpoints to adjust for both sampling bias and the evident skewness of the estimator's bootstrap distribution. Which resampling strategy best satisfies these requirements?
Fit an exponential distribution to the original data and draw 10 000 parametric bootstrap samples from that fitted model to build the interval.
Generate 1 000 resamples, record the median in each, and take the 2.5th and 97.5th percentiles of that distribution without any further adjustment (standard percentile bootstrap).
Apply a natural-log transform, compute a Student's t 95 % interval for the transformed sample mean, then exponentiate the endpoints to approximate a median interval.
Generate at least 1 000 resamples of the data and construct a bias-corrected and accelerated (BCa) percentile interval for the sample median.
The bias-corrected and accelerated (BCa) bootstrap first estimates a bias-correction factor (z0) and an acceleration term (a) from the data, then maps these into adjusted percentile cut-offs. Because it explicitly corrects for bias and for skewness in the bootstrap distribution, BCa intervals achieve more accurate coverage for asymmetric statistics such as the sample median drawn from a skewed population. A standard percentile bootstrap does not correct for either bias or skewness, so its coverage can be poor when the statistic's sampling distribution is asymmetric. A parametric bootstrap that assumes an exponential (or any other) model violates the analyst's stated goal of avoiding distributional assumptions. Finally, back-transforming a Student's t interval around the log-mean targets the mean on the transformed scale, not the median on the original scale, and still relies on normality after transformation. Therefore, constructing a BCa percentile interval from non-parametric resamples is the most appropriate choice.
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What is a BCa (Bias-Corrected and Accelerated) percentile interval?
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Why does the standard percentile bootstrap fail in skewed distributions?
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What are the limitations of using a parametric bootstrap for this scenario?