Local GMM estimation via DNN rank weights

Estimates a local parameter by solving a two-step GMM problem after localizing observations with DNN rank weights. The first step uses an identity moment weighting matrix; the second step uses the local moment covariance estimated at the first-step solution.

Usage

gmm_dnn(
  data = NULL,
  x_cols = NULL,
  X = NULL,
  X0 = NULL,
  x0 = NULL,
  model,
  model_data = NULL,
  distance = "l2",
  method = c("exact", "asymp"),
  k = 1L,
  s = NULL,
  tuning = NULL,
  normalize = TRUE,
  start = NULL,
  optimizer = c("BFGS", "Nelder-Mead", "L-BFGS-B"),
  jacobian = c("auto", "analytic", "fd"),
  omega_ridge = 1e-08,
  fd_step = 1e-05,
  se = TRUE,
  ctx = NULL,
  return = c("W")
)

Arguments

data: Optional data frame containing covariates and model variables. Column names must be non-missing, non-empty, and unique.
x_cols: Names or indices of covariate columns in data.
X: Numeric n x p covariate matrix for the matrix interface.
X0: Numeric matrix of target points; mutually exclusive with x0.
x0: Numeric vector for one target point.
model: A new_gmm_model() object.
model_data: Optional model data used with the matrix interface.
distance: Distance name or specification.
method: One of "exact" or "asymp" for DNN weights.
k: Integer DNN neighbour count inside each size-s subsample. The paper theory uses k = 1 (the default).
s: Integer kernel order (undersmoothing parameter), or NULL. When both s and tuning are NULL (the default), s is resolved from the paper undersmoothing rule tuning_dnn_paper(), \(s = \lfloor 0.4 n^{(k_x+1)/(k_x+2)} \rfloor\). Note that small fixed values such as s = 1 (or k = s) yield uniform weights and hence no localization; a warning is emitted in that case.
tuning: Optional kernel-order tuning specification. When supplied, s must be omitted.
normalize: Logical; normalize weight columns to sum to one.
start: Optional numeric vector of length p_theta, or p_theta x m matrix, used as optimizer starts.
optimizer: Optimizer method passed to stats::optim().
jacobian: One of "auto", "analytic", or "fd".
omega_ridge: Non-negative ridge multiplier for local moment covariance.
fd_step: Positive finite finite-difference step multiplier.
se: Logical; compute sandwich standard errors.
ctx: Optional context passed to distance and ranking components.
return: Optional extras: c("W", "ranks", "ord", "dx", "g_obs", "omega", "jacobian", "ess", "neighbors", "tuning"). The neighbors extra returns the first k nearest observations used inside each size-s subsample, not the full DNN weight support.

Value

A gmm_result object with estimates, diagnostics, metadata, the m x p evaluation-point matrix x0 (with covariate column names propagated from the training data when available), and requested extras.

Details

Two interfaces are supported.

Data-frame interface: pass data, x_cols, and a gmm_model.
Matrix interface: pass X, one of X0 or x0, a gmm_model, and model_data when the model needs observation-level variables.

Nuisance quantities are not fit internally. They must be supplied to the model through data or model_data.

Exact DNN localization uses the full rank permutation at each target rather than an s-nearest-neighbor truncation. For exact DNN fits, the finite-population support edge is rank n - s + k, not rank s.

Examples

dgp <- sim_iv_data("dgp2_iv_homog_overid", n = 120, kx = 2, q = 2, seed = 1)
model <- gmm_model_dr_iv(
  z_cols = c("Z1", "Z2"),
  pi_cols = c("piZ1_oracle", "piZ2_oracle"),
  muY_col = "muY_oracle",
  muD_col = "muD_oracle"
)
fit <- gmm_dnn(
  data = dgp$data,
  x_cols = c("X1", "X2"),
  x0 = dgp$x0,
  model = model,
  k = 1, s = 10,
  return = "ess"
)
fit$theta
#>       target_1
#> theta 1.196561