cram_variance_estimator_policy_value

This function estimates the asymptotic variance of the cram estimator
for the policy value (psi).

Performs the Cram method, a general and efficient approach to simultaneous learning and evaluation using a generic machine learning algorithm. In a single pass of batched data, the proposed method repeatedly trains a machine learning algorithm and tests its empirical performance. Because it utilizes the entire sample for both learning and evaluation, cramming is significantly more data-efficient than sample-splitting. Unlike cross-validation, Cram evaluates the final learned model directly, providing sharper inference aligned with real-world deployment. The method naturally applies to both policy learning and contextual bandits, where decisions are based on individual features to maximize outcomes. The package includes cram_policy() for learning and evaluating individualized binary treatment rules, cram_ml() to train and assess the population-level performance of machine learning models, and cram_bandit() for on-policy evaluation of contextual bandit algorithms. For all three functions, the package provides estimates of the average outcome that would result if the model were deployed, along with standard errors and confidence intervals for these estimates. Details of the method are described in Jia, Imai, and Li (2024) <https://www.hbs.edu/ris/Publication%20Files/2403.07031v1_a83462e0-145b-4675-99d5-9754aa65d786.pdf> and Jia et al. (2025) <doi:10.48550/arXiv.2403.07031>.

Yanis Vandecasteele

cramR

Cram Method for Efficient Simultaneous Learning and Evaluation

cram_variance_estimator_policy_value function

<dl><dt>X</dt>
<dd>A matrix or data frame of covariates for each sample.</dd>
<dt>Y</dt>
<dd>A vector of outcomes for the n individuals.</dd>
<dt>D</dt>
<dd>A vector of binary treatments for the n individuals.</dd>
<dt>pi</dt>
<dd>A matrix of n rows and (nb_batch + 1) columns,
where n is the sample size and nb_batch is the number of batches,
containing the policy assignment for each individual for each policy.
The first column represents the baseline policy.</dd>
<dt>batch_indices</dt>
<dd>A list where each element is a vector of indices corresponding to the individuals in each batch.</dd>
<dt>propensity</dt>
<dd>Propensity score function</dd></dl>

Arguments

Cram Policy: Variance Estimate of the crammed Policy Value estimate (Psi) — cram_variance_estimator_policy_value

<dl>

<dt>X</dt>
<dd>A matrix or data frame of covariates for each sample.</dd>


<dt>Y</dt>
<dd>A vector of outcomes for the n individuals.</dd>


<dt>D</dt>
<dd>A vector of binary treatments for the n individuals.</dd>


<dt>pi</dt>
<dd>A matrix of n rows and (nb_batch + 1) columns,
where n is the sample size and nb_batch is the number of batches,
containing the policy assignment for each individual for each policy.
The first column represents the baseline policy.</dd>


<dt>batch_indices</dt>
<dd>A list where each element is a vector of indices corresponding to the individuals in each batch.</dd>


<dt>propensity</dt>
<dd>Propensity score function</dd>

</dl>

cram_variance_estimator_policy_value: Cram Policy: Variance Estimate of the crammed Policy Value estimate (Psi)

Description

Usage

Value

Arguments