dualbounds.generic.plug_in_no_covariates¶

dualbounds.generic.plug_in_no_covariates(outcome: array, treatment: array, f: callable, propensities: array | None = None, clusters: array | None = None, B: int = 0, verbose: bool = True, alpha: float = 0.05, max_nvals: int = 1000, _which_bound='both') → dict[source]¶

Computes plug-in bounds on \(E[f(Y(0),Y(1))]\) without using covariates.

Parameters:¶

outcome : np.array¶

n-length array of outcomes (y)

treatment : np.array¶

n-length array of treatments (W).

f : function¶

f(y0, y1, x) defines the objective.

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).

verbose : bool¶

Show progress bar while bootstrapping if verbose=True.

alpha : float¶

nominal Type I error level.

max_nvals : int¶

Maximum dimension of optimal transport problem.

_which_bound : str¶

One of ‘both’, ‘lower’, ‘upper’.

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.

These arrays will be length 1 (instead of 2) if which_bound != ‘both’.

Return type:¶

dict