12  Bootstrap variants & clustering

13 Bootstrap variants & clustering

didgpu supports two bootstrap kinds for didgpu_cs() and didgpu_fect():

Kind	Description	When to use
"cluster"	unit-level resampling, fit refit per replicate	classical, agnostic about the inference. Slow at large B.
"multiplier"	influence-function multiplier on per-unit IFs	much faster (no refit per replicate). Requires the IF representation, which all estimators in didgpu have.

For didgpu() only the cluster bootstrap is supported (the dynamic estimator’s IFs require additional work that is on the roadmap).

13.1 Specifying a cluster

By default the bootstrap clusters on the unit:

fit <- didgpu(..., bootstrap_reps = 500)

If your unit is not the natural cluster (panel of student outcomes where the policy varies at the school level, etc.), pass cluster:

fit <- didgpu(
  panel, ...,
  cluster        = "school_id",
  bootstrap_reps = 500
)

13.2 Resampling at multiple levels

For multi-way clustering (e.g. classroom-within-school), use a composite cluster id:

panel$cluster_composite <- paste(panel$school_id, panel$classroom_id, sep = ":")
fit <- didgpu(panel, ..., cluster = "cluster_composite", bootstrap_reps = 500)

didgpu’s resampler is a 1-pass random hash of clusters → reps, so it scales linearly in B.

13.3 Multiplier bootstrap

cs <- didgpu_cs(
  panel, ...,
  est_method     = "DR",
  bootstrap_reps = 5000,
  bootstrap_kind = "multiplier",
  seed           = 17
)

This is the fast variant. It uses per-unit influence functions \(\psi_i\) and Rademacher / Mammen multipliers \(\xi_b\):

\[ \hat\theta^{(b)} - \hat\theta \approx \frac{1}{n} \sum_i \xi_b \, \psi_i \]

On the GPU, all of this is a couple of GEMVs and a Cholesky per multiplier — vastly faster than refitting the inner estimator 5000 times.

Tip

A worked example comparing cluster and multiplier bootstrap SEs on the same panel (they agree to ~1e-2 at B = 2000) is in progress.