Signed Wald intersection test

Calculating test statistics and p-values for the signed Wald intersection test given by $$SW = \inf_{\theta \in \cap_{i=1}^n H_i} \{(\widehat{\theta}-\theta)^\top W\widehat{\Sigma}W (\widehat{\theta}-\theta)\} $$ with individual hypotheses for each coordinate of $\theta$ given by $H_i: \theta_j < \delta_j$ for some non-inferiority margin $\delta_j$, $j=1,\ldots,n$. #

Usage

test_intersection_sw(
  par,
  vcov,
  noninf = 0,
  weights = 1,
  nsim.null = 10000,
  index = NULL,
  control = list(),
  par.name = "theta"
)

Arguments

par: (numeric) parameter estimates or estimate object
vcov: (matrix) asymptotic variance estimate
noninf: (numeric) non-inferiority margins
weights: (numeric) optional weights
nsim.null: (integer) number of sample used in Monte-Carlo simulation
index: (integer) subset of parameters to test
control: (list) arguments to alternating projection algorithm. See details section.
par.name: (character) parameter names in output

Value

htest object

Details

The constrained least squares problem is solved using Dykstra's algorithm. The following parameters for the optimization can be controlled via the control list argument: dykstra_niter sets the maximum number of iterations (default 500), dykstra_tol convergence tolerance of the alternating projection algorithm (default 1e-7), pinv_tol tolerance for calculating the pseudo-inverse matrix (default length(par).Machine$double.epsmax(eigenvalue)).

References

Christian Bressen Pipper, Andreas Nordland & Klaus Kähler Holst (2025) A general approach to construct powerful tests for intersections of one-sided null-hypotheses based on influence functions. arXiv: https://arxiv.org/abs/2511.07096.

Author

Klaus Kähler Holst, Christian Bressen Pipper

Examples

S <- matrix(c(1, 0.5, 0.5, 2), 2, 2)
thetahat <- c(0.5, -0.2)
test_intersection_sw(thetahat, S, nsim.null = 1e5)
#> 
#> 	Signed Wald Intersection Test
#> 
#> data:  
#> Intersection null hypothesis: theta =< [0, 0]
#> w = [0.5, 0.5]
#> Q = 0.0625, p-value = 0.479
#> 
test_intersection_sw(thetahat, S, weights = NULL)
#> 
#> 	Signed Wald Intersection Test
#> 
#> data:  
#> Intersection null hypothesis: theta =< [0, 0]
#> w = [0.5, 0.5]
#> Q = 0.0625, p-value = 0.465
#> 

if (FALSE) { # \dontrun{
# only on 'lava' >= 1.8.2
e <- estimate(coef = thetahat, vcov = S, labels = c("p1", "p2"))
lava::closed_testing(e, test_intersection_sw, noninf = c(-0.1, -0.1)) |>
  summary()
} # }