Methods Guide
IID Methods
Percentile
Standard quantile-based CI. Simple but can have poor coverage for skewed distributions.
Basic (Reverse Percentile)
BCa (Bias-Corrected and Accelerated)
The recommended default. Corrects for bias and skewness using jackknife acceleration:
Studentized (Bootstrap-t)
Uses pivotal quantity \(t^* = (\hat{\theta}^* - \hat{\theta}) / \hat{se}^*\) with nested bootstrap for SE.
Poisson Bootstrap
Weighted resampling with \(W \sim \text{Poisson}(1)\). Ideal for streaming/online algorithms.
Bernoulli Bootstrap
Binary weights \(W \sim \text{Bernoulli}(p)\). Useful for specific ML applications.
Subsampling (m-out-of-n)
Sampling without replacement, size \(m < n\). Required for non-regular statistics (max, min).
Time Series Methods
Moving Block Bootstrap (MBB)
Overlapping fixed-length blocks. Set block_length based on autocorrelation structure.
Circular Block Bootstrap (CBB)
Wraps data circularly to eliminate edge effects. Same block logic as MBB.
Stationary Bootstrap (Politis & Romano)
Random block lengths \(L \sim \text{Geometric}(1/\bar{L})\) where \(\bar{L}\) = mean_block.
Tapered Block Bootstrap
Applies a tapering window (Tukey, Hanning, etc.) to each block. For spectral density estimation.
AR-Sieve Bootstrap
Fits AR(p) model → extracts residuals → resamples residuals → reconstructs series.
Wild Bootstrap
$\(y_t^* = \hat{y}_t + \hat{\varepsilon}_t \cdot v_t\)$ where \(v_t\) is Rademacher (±1) or Mammen two-point. Handles heteroskedasticity.
Hierarchical Methods
Cluster Bootstrap
Resamples entire clusters (groups), preserving within-group correlation structure.
Stratified Bootstrap
Resamples within each stratum independently, preserving class proportions.