dualbounds.lee.lee_bound_no_covariates¶

dualbounds.lee.lee_bound_no_covariates(outcome: array, treatment: array, selections: array, propensities: array | None = None, clusters: array | None = None, B: int = 200, alpha: float = 0.05, verbose=False)[source]¶

Computes plug-in Lee bounds without using covariates.

Parameters:¶

outcome : np.array¶

n-length array of outcomes (y)

treatment : np.array¶

n-length array of treatments (W).

selections : np.array¶

n-length array of selection indicators (S).

propensities : np.array¶

n-length array of propensity scores (pis). Default: all equal to treatment.mean().

clusters : np.array¶

Optional n-length array of clusters, so clusters[i] = j indicates that observation i is in cluster j.

B : int¶

Number of bootstrap replications to compute standard errors. Defaults to 0 (no standard errors).

alpha : float¶

nominal Type I error level.

verbose : bool¶

Show progress bar while bootstrapping if verbose=True.

Returns:¶

results – Dictionary containing up to three keys:

• estimates: 2-length array of lower/upper estimates.

• ses: 2-length array of lower/upper standard errors.

• cis: 2-length array of lower/upper confidence intervals.

Return type:¶

dict