Bandwidth Selection for R3D

Computes bandwidth(s) for local polynomial estimation in a regression discontinuity setting with distribution-valued outcomes. Implements a three-step pilot procedure to find either MSE-optimal (per-quantile) bandwidths or a single IMSE-optimal bandwidth, depending on method. For details, see the Appendix of vandijcke2025;textualR3D.

r3d_bwselect(
  X,
  Y_list,
  T = NULL,
  q_grid = seq(0.1, 0.9, 0.1),
  method = c("simple", "frechet"),
  s = 1,
  p = 2,
  kernel = function(u) pmax(0, 1 - abs(u)),
  cutoff = 0,
  fuzzy = FALSE,
  coverage = FALSE,
  ...
)

Arguments

X: Numeric vector of the running variable.
Y_list: A list of numeric vectors; each entry is the sample of outcomes from one unit's distribution.
T: (Optional) Numeric or logical vector of treatment statuses for fuzzy design.
q_grid: Numeric vector of quantiles at which local polynomial fits are performed.
method: Either "simple" (per-quantile MSE-optimal) or "frechet" (single IMSE-optimal bandwidth).
s: Integer specifying the order of local polynomial in the pilot stage (often 1).
p: Integer specifying the final local polynomial order (often 2).
kernel: Kernel function for local weighting. Defaults to triangular kernel.
cutoff: Numeric scalar threshold. Data are recentered so X - cutoff has cutoff at 0.
fuzzy: Logical indicating fuzzy design. Default is FALSE.
coverage: Logical indicating whether to apply the coverage correction rule of thumb of calonico2018effect;textualR3D. Default is FALSE.
...: Additional arguments for future expansions.

Value

A list with elements:

method: Method used: "simple" or "frechet".
q_grid: Input q_grid.
h_star_num: Bandwidth(s) for numerator (outcome).
h_star_den: Bandwidth for denominator (treatment, if fuzzy).
pilot_h_num: Pilot bandwidth(s) for numerator.
pilot_h_den: Pilot bandwidth for denominator (if fuzzy).
s, p: Polynomial orders.
B_plus, B_minus: Bias estimates for numerator.
V_plus, V_minus: Variance estimates for numerator.
f_X_hat: Estimated density of \(X\) at cutoff.

Details

Implements a three-step procedure:

Estimates \(f_X(0)\) using Silverman’s rule and computes pilot bandwidths via global polynomials.
Runs pilot local polynomial regressions to estimate bias and variance.
Computes MSE-optimal (per-quantile) or IMSE-optimal (single) bandwidths.

In fuzzy RDD, separate bandwidths are computed for the numerator (outcome) and denominator (treatment).

Arguments

Value

Details

References