Pair-copula selection

Automatic pair selection evaluates a candidate family set, optional rotations, and optional independence, then chooses the smallest model-selection score.

fit(
    PairCopula,
    U;
    family_set=:default,
    pair_method=:mle,
    selection_criterion=:bic,
    allow_rotations=true,
    preselect=true,
    include_independence=true,
)

Criteria

• :loglik selects the largest fitted log-likelihood.

• :aic minimizes  .

• :bic minimizes  .

Here is the number of pair-copula parameters and is the number of observations.

Family sets

• family_set=:default uses the validated default parametric set.

• family_set=:all uses the broader parametric set.

• A tuple or vector gives complete control over the candidates.

Preselection

preselect=true currently prunes impossible rotation signs using empirical dependence. It is intentionally simpler than vinecopulib's full family-preselection heuristics. Correctness parity benchmarks disable preselection so both engines search the same explicit candidate space.