Compute Quadratic Coefficients for CI (Stratified Asymmetric)

Source: R/inference.R

Calculates the coefficients \((a, b, c)\) for the confidence interval quadratic inequality in a general design that includes both grouping (stratification) and covariates. This function is optimized for designs where projection matrices are block-diagonal with respect to groupW but potentially asymmetric within blocks due to covariate adjustments.

GetL3OCIcoef_fast(
  df,
  groupW,
  groupQ,
  X,
  Y,
  MX,
  MY,
  q = qnorm(0.975)^2,
  noisy = FALSE
)

Arguments

df

Data frame. Contains the observable variables and grouping indicators.

groupW

Column name (unquoted). The covariate stratification variable.

groupQ

Column name (unquoted). The instrument grouping variable.

X

Column name (unquoted). The endogenous regressor.

Y

Column name (unquoted). The outcome variable.

MX

Column name (unquoted). Leverage-adjusted regressor (\(M X\)).

MY

Column name (unquoted). Leverage-adjusted outcome (\(M Y\)).

q

Numeric scalar. The critical value for test inversion (typically \(1.96^2\)). Defaults to qnorm(.975)^2.

noisy

Logical. If TRUE, prints progress. Defaults to FALSE.

Value

Numeric vector of length 3 containing c(a, b, c).

Details

This function performs a loop:

  1. Splits data by groupW. Computes local projection matrices \(P_Q\) and \(P_W\) for each stratum.

  2. Calculates the full UJIVE weighting matrix \(G = U(P_Q) - U(P_W)\) locally. Since \(G\) is asymmetric, it computes all 5 variance components.

  3. Accumulates all polynomial coefficients for \(\hat{V}(\beta)\) simultaneously using extensive pre-calculation of vector products.

References

Yap, L. (2025). "Inference with Many Weak Instruments and Heterogeneity". Working Paper.