copula_spec_test: Specification test for a parametric copula of the private...

In qdfauction: Nonparametric Quantile Density Estimation and Structural Analysis of First-Price Auctions

Specification test for a parametric copula of the private values

Description

Tests whether an exchangeable Archimedean copula family is compatible with the bids, using T = \sup_u |\hat\psi_{NP}(u) - \psi(u; \hat\theta)| over a grid of interior quantiles (Doosti 2026a), where \hat\psi_{NP} is [copula_psi_np()] and \hat\theta is the pseudo-maximum-likelihood estimate of [copula_fit()]. Critical values come from a parametric bootstrap under the null: rank matrices are simulated from the fitted copula, the parameter is re-estimated and the statistic recomputed. Because both multipliers depend on the bids only through their ranks, the test does not involve the marginal distribution.

Usage

copula_spec_test(
  bids,
  family = c("clayton", "gumbel", "frank", "independence"),
  B = 199,
  grid = seq(0.1, 0.9, by = 0.02),
  b = NULL
)

Arguments

bids	an 'L' by 'n' matrix or data frame of bids.
family	'"clayton"', '"gumbel"', '"frank"' or '"independence"'.
B	number of bootstrap replications.
grid	interior quantiles over which the supremum is taken.
b	beta-kernel bandwidth, see [copula_psi_np()].

Value

an object of class '"htest"' with the statistic, the bootstrap p-value and the fitted parameter.

Reproducibility

Call [set.seed()] beforehand to make the bootstrap reproducible.

Examples

set.seed(1)
U <- rcopula_archimedean(150, 3, "gumbel", theta = 2)
copula_spec_test(U, "gumbel", B = 99)
copula_spec_test(U, "independence", B = 99)

qdfauction documentation built on Nov. 10, 2026, 5:07 p.m.