BCabootstrap

BCabootstrap is a bootstrap-based statistical method used to construct confidence intervals for a statistic by applying the bias-corrected and accelerated (BCa) adjustment. It is employed when analytic formulas for the sampling distribution are unavailable or unreliable, especially for nonparametric or skewed data.

The BCa approach starts with a primary statistic computed from the original sample. A large number of bootstrap resamples are drawn with replacement, and the statistic is computed for each resample to form an empirical bootstrap distribution. Two adjustments are then estimated: a bias-correction term that accounts for skewness in the bootstrap distribution, and an acceleration term that reflects the rate of change of the distribution with respect to the underlying data (often estimated with jackknife influence values). These terms are combined to produce adjusted percentile points, which yield the BCa confidence limits.

Compared with basic percentile bootstrap intervals, BCabootstrap aims to provide more accurate coverage by compensating for bias and skewness in the statistic’s distribution. It is particularly useful for small samples, statistics with skewed sampling distributions, or situations where variance is unstable. The method is widely implemented in statistical software as part of bootstrap facilities and can be applied to a broad range of statistics, including means, medians, regression coefficients, and more complex estimators.

Limitations include increased computational demand due to the large number of resamples, sensitivity to outliers, and potential instability in the acceleration estimate when the sample size is very small. Proper application also relies on the quality of the original data and the suitability of resampling assumptions for the problem at hand.