Confidence bands for parameter vectors — confidence

Computes simultaneous confidence bands that provide coverage for the entire parameter vector, adjusting for multiple comparisons. The formula is: $$\hat{\theta} \pm \hat{c}_{\alpha/2} \times \widehat{SE}(\hat{\theta})$$ where $\hat{c}$ is the adjusted critical value.

Usage

confidence_bands(
  object,
  alpha = 0.05,
  method = "supt",
  n_draws = 100000L,
  seed = NULL,
  subset = NULL,
  covariance = NULL,
  ...
)

Arguments

object: A fitted MEstimator object, or a numeric vector of parameter estimates.
alpha: Numeric significance level, between 0 and 1. Default 0.05.
method: Character string. "supt" (default) for supremum-t or "bonferroni" for Bonferroni correction.
n_draws: Integer number of MVN draws for the sup-t method. Default 1e5. The critical value is a Monte Carlo estimate of a fixed sup-t quantile, and at 1e5 draws the band half-width varies by roughly 0.2% across independent draws, which is negligible relative to the band width. Python's estimator method defaults to 1e6; both defaults target the same quantity and agree to within Monte Carlo error, so deli keeps the smaller default for faster computation. Set n_draws = 1e6 to match Python's estimator default. Note that seeded band values are not reproducible across the two languages because the MVN samplers differ.
seed: Integer seed for reproducibility. Default NULL.
subset: Integer vector of parameter indices to compute bands for. Default NULL (all parameters).
covariance: Numeric covariance matrix (only when object is numeric).
...: Not used. Must be empty, so a name that is not one of the documented arguments is an error rather than silently ignored.

Value

A p-by-2 matrix with columns "lower" and "upper". For a fitted estimator the rows are named for the parameters, as in confint(). For a numeric object they take their names from it, when it has any.

Examples

# Two independent samples, each contributing one mean parameter
set.seed(42)
n <- 200
y1 <- rnorm(n, 2)
y2 <- rnorm(n, 3)

psi <- function(theta) {
  rbind(y1 - theta[1], y2 - theta[2])
}

m <- m_estimate(stacked_equations = psi, init = c(0, 0))

# Simultaneous bands cover both means at once, so they are wider than the
# pointwise intervals from confint(m)
confidence_bands(m, method = "supt", seed = 1)
#>            lower    upper
#> theta_1 1.818388 2.126643
#> theta_2 2.861506 3.161062