Asymptotic Calibration Check for RESI Variance Estimates

Runs a plasmode simulation to verify that the asymptotic normal CI machinery is correctly calibrated for all four model settings (lm/glm x parametric/robust). For each (setting, sample size) cell the function checks:

1. Bias(theta): \(\hat\theta \to \theta_{\rm true}\) – raw coefficients (and \(\phi = \hat\sigma^2\) for lm) converge to the full-dataset values.

2. vcov check A (estimator consistency): \(n \cdot \bar V_{\rm analytic} / (n_{\rm full} \cdot V_{\rm true}) \to 1\).

3. vcov check B (calibration): \(n \cdot \widehat{\rm Var}(\hat\beta) / (n_{\rm full} \cdot V_{\rm true}) \to 1\).

4. Bias(R): RESI point estimates converge to the full-dataset values.

5. sigma2S check A (estimator consistency): \(\bar{\hat\sigma}^2_S / \sigma^2_{S,\rm true} \to 1\).

6. sigma2S check B (CI calibration): \(n \cdot \widehat{\rm Var}(\hat R) / \sigma^2_{S,\rm true} \to 1\).

True values are taken from the full insurance dataset using the same definitions as insurancePlasmodeSim. \(\sigma^2_S\) is extracted from the asymptotic-normal CI half-width: \(\hat\sigma^2_S = n \cdot ({\rm hw}/z_{\alpha/2})^2\).

Usage

simCalibrationSim(
  nsim = 500L,
  n.vec = c(100L, 200L, 500L, 1000L, 2000L, 5000L),
  alpha = 0.05,
  output.dir = "resiCalibrationSim",
  fixed.knots = FALSE,
  mc.cores.reps = 1L
)

Arguments

nsim

Integer, replicates per (setting, \(n\)) cell. Default 500.

n.vec

Integer vector of sample sizes. Default c(100, 200, 500, 1000, 2000, 5000).

alpha

Numeric, nominal CI level. Default 0.05.

output.dir

Character, directory for raw per-cell RDS files. Default "resiCalibrationSim".

fixed.knots

Logical. Fix spline knots at full-dataset quantiles. Default FALSE.

mc.cores.reps

Integer, cores for within-cell parallelism. Default 1.

Value

Invisibly returns the combined metrics data.frame.

See also

insurancePlasmodeSim, simCompareMethodsFigures