Calculates the coefficients \((a, b, c)\) of the quadratic inequality \(a\beta^2 + b\beta + c \leq 0\) used to construct confidence intervals for \(\beta\) in the grouped design setting (no covariates). This function inverts the UJIVE/LIML score test using optimized variance estimators for block-diagonal designs.
GetCIcoef_nocov(df, groupZ, X, Y, MX, MY, q = qnorm(0.975)^2, noisy = FALSE)Data frame. Contains the observable variables \(X, Y\) and their projections.
Column name (unquoted). The instrument grouping variable.
Column name (unquoted). The endogenous regressor.
Column name (unquoted). The outcome variable.
Column name (unquoted). Leverage-adjusted regressor (\(M X\)).
Column name (unquoted). Leverage-adjusted outcome (\(M Y\)).
Numeric scalar. Critical value for the test inversion (e.g., \(1.96^2\)).
Defaults to qnorm(.975)^2 (approx. 3.84) for a 95 percent confidence interval.
Logical. If TRUE, prints progress dots during calculation.
Defaults to FALSE.
Numeric vector of length 3 containing c(a, b, c).
This function performs the same logic as GetCIcoef but is specifically
appropriate for designs where instruments form mutually exclusive groups
and no global covariates link them.
The returned coefficients define the confidence set: $$\{ \beta : (P_{XX}^2 - q C_2)\beta^2 + (-2 P_{XY} P_{XX} - q C_1)\beta + (P_{XY}^2 - q C_0) \leq 0 \}$$
Yap, L. (2025). "Inference with Many Weak Instruments and Heterogeneity". Working Paper.