Fail-safe for small group sizes in bootstrap and confidence interval calculations

[wlangera]

Description

Currently, bootstrap_cube() and calculate_bootstrap_ci() allow uncertainty estimation for groups with very small sample sizes. This can lead to:

• undefined jackknife estimates (BCa acceleration), --> Creates error now
• degenerate or misleading bootstrap distributions,
• confidence intervals that are numerically computable but statistically meaningless.

In particular:

• BCa intervals are mathematically undefined for groups with too few observations.
• Percentile, normal, and basic intervals are technically computable but unreliable when group sizes are very small.

To ensure statistically defensible output, a fail-safe mechanism should be implemented.

Proposed behaviour

Global rule:

• If a group has fewer than 4 original observations,
  → all confidence intervals (perc, bca, norm, basic) must be returned as NA
  → a warning must be issued.

This rule applies consistently across:

• bootstrap generation (bootstrap_cube()), and
• uncertainty estimation (calculate_bootstrap_ci()).

Implementation notes

• Group size (n_group) should be:

  • computed during bootstrapping, and
  • carried through to downstream CI calculations.

• CI calculation should short-circuit early for invalid groups, rather than:

  • failing deep inside BCa acceleration logic, or
  • silently returning misleading intervals.

• BCa-specific failures (e.g. undefined acceleration) should become secondary once the group-size rule is enforced.

Rationale

• Resampling methods cannot create information that is not present in the data.
• For very small groups, uncertainty estimates are dominated by numerical artefacts rather than sampling variability.
• Returning NA with an explicit warning is more honest and policy-safe than producing fragile confidence limits.

This behaviour aligns with:

• best practices in bootstrap inference (Efron & Tibshirani),
• reproducibility and transparency requirements for indicator reporting,
• downstream policy and monitoring use cases.

Acceptance criteria

• Groups with n_group < 4 return NA for all CI types
• A clear warning is issued once per call
• Behaviour is documented
• Unit tests cover small-group cases