Bootstrap Confidence Intervals (BCa)

The bias-corrected and accelerated (BCa) bootstrap confidence interval adjusts percentile bootstrap limits for median bias and for skewness of the statistic's sampling distribution, estimated by the jackknife.

BCa 부트스트랩 신뢰구간은 재표집 분포의 백분위 구간을 편향과 치우침(가속 상수)으로 보정해, 정규분포를 가정하지 않고도 정확한 구간을 얻는 방법이다.

How can I get a confidence interval for a median or a skewed mean without assuming normality?

정규분포를 가정하지 않고 중앙값이나 치우친 평균의 신뢰구간을 구하려면 어떻게 하나요?

The BCa bootstrap resamples the data many times, computes the statistic in each resample, and reads the interval limits from adjusted percentiles of that distribution. The adjustments correct for bias and skewness, giving more accurate coverage than the simple percentile interval.

When to use Bootstrap Confidence Intervals (BCa)

• The statistic has no simple standard-error formula, such as a median
• The data are skewed and normal-theory intervals are doubtful
• You want a confidence interval for a difference between two groups' medians or SDs

When to use something else

• The sample is very small (under about 15); use exact or parametric methods instead
• Observations are dependent, such as time series; use a block bootstrap instead

Assumptions and requirements

• Observations are independent and identically distributed
• The sample is representative of the population
• The statistic is reasonably smooth in the data
• The statistic is the mean, median or SD, or its difference between two groups

What the analysis reports

• Point estimate
• BCa confidence interval
• Percentile interval for comparison
• Bootstrap standard error and bias

How to report it

The [statistic] was [value], 95% BCa bootstrap CI [[value], [value]], based on [B] resamples.

Related methods

• Jackknife Estimation
• Robust Location and Scale Estimates

Run Bootstrap Confidence Intervals (BCa) on Quorant