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Asymptotic \(U_n\) Statistic (Finite-Difference Calibration)

Source: R/paper_figures.R
simplex_Un_asymptotic.Rd

Computes the \(U_n\) statistic using the finite-difference gradient \(J\), which gives the correct asymptotic variance for the simplex class. This is the version whose null distribution is studied in the simulation section of the companion paper (Figure 1).

Usage

simplex_Un_asymptotic(y, X, Z = NULL, eps = 1e-04)

Arguments

y

Response vector in (0, 1).

X

Design matrix for the mean sub-model.

Z

Design matrix for the dispersion sub-model (or NULL).

eps

Finite-difference step. Default 1e-4.

Value

Scalar \(U_n\) (asymptotic calibration), or NA if the model fails to converge.

Details

For the bootstrap test, use simplex_gof instead — the analytic gradient is bootstrap-invariant and faster.

See also

simplex_gof, simplex_diag

Examples

set.seed(1)
n  <- 40
X  <- cbind(1, matrix(runif(n * 4), n, 4))
mu <- plogis(drop(X %*% c(2, -0.5, -1.4, 1.25, -2.35)))
y  <- rsimplex(n, mu, 0.5)
Un <- simplex_Un_asymptotic(y, X)
Un
#> [1] 1.531058