Construct a RAL Inference Object

Creates a regular asymptotically linear (RAL) inference object from pre-computed influence functions. This is the base class for all influence-function-based inference in ddml.

Usage

ral(
  coefficients,
  inf_func,
  dinf_dtheta = NULL,
  nobs,
  coef_names,
  cluster_variable = NULL,
  estimator_name = "RAL estimator",
  subclass = NULL,
  ...
)

Arguments

coefficients: A $p \times$ nfit matrix of estimated coefficients. Rows are parameters, columns are fits (e.g., ensemble types).
inf_func: A 3D array of dimension $n \times p \times$ nfit. The influence function evaluated at each observation.
dinf_dtheta: Optional 4D array of dimension $n \times p \times p \times$ nfit. The derivative of the influence function with respect to $\theta$, used for HC3 leverage. If NULL, HC3 is unavailable.
nobs: Integer number of observations.
coef_names: Character vector of parameter names (length $p$).
cluster_variable: Optional vector of cluster identifiers (length $n$). If non-NULL, cluster-robust inference is used.
estimator_name: Character string for display.
subclass: Optional character string prepended to the class vector.
...: Additional named elements stored in the object.

Value

An object of class ral (or c(subclass, "ral")).

Details

A regular asymptotically linear (RAL) estimator $\hat\theta$ satisfies

$$\hat\theta - \theta_0 = \frac{1}{n} \sum_{i=1}^{n} \phi(W_i; \theta_0) + o_p(n^{-1/2}),$$

where $\phi(W_i; \theta_0)$ is the influence function. This package stores the estimated influence function $\hat\phi_i \equiv \phi(W_i; \hat\theta)$ in the inf_func slot.

When an observation-level derivative $\partial \hat\phi_i / \partial \theta$ is available (stored in dinf_dtheta), the estimator supports HC3 inference via leverage; see hatvalues.ral.

The RAL framework is estimator-agnostic: it consumes pre-computed influence functions and does not prescribe how they are obtained. For the specific construction under cross-fitting and Neyman-orthogonal scores, see ddml-intro. For linear combinations of ddml estimators, see lincom.