cleverly.sensitivity.SensitivityElements#

class cleverly.sensitivity.SensitivityElements(estimand: str, sigma2: float, nu2: float, max_bias: float, psi_sigma2: ndarray[tuple[Any, ...], dtype[float64]], psi_nu2: ndarray[tuple[Any, ...], dtype[float64]] | None, psi_max_bias: ndarray[tuple[Any, ...], dtype[float64]] | None, riesz_representer: ndarray[tuple[Any, ...], dtype[float64]], nu2_estimator: str)[source]#

The ingredients of the bias bound for one estimand.

Parameters:

estimandstr: Alias of the estimand these elements describe.
sigma2float: \(E[(Y - \bar Q^*(A, W))^2]\), the residual outcome variance.
nu2float: \(E[\alpha(A, W)^2]\), the second moment of the Riesz representer.
max_biasfloat: \(\sqrt{\sigma^2 \nu^2}\), the bias scale. The bound multiplies it by |rho| sqrt(cf_y cf_d / (1 - cf_d)), which can exceed 1, so it is not the largest bias. The name follows DoubleML.
psi_sigma2ndarray: Influence curve of sigma2.
psi_nu2ndarray or None: Influence curve of nu2 under the doubly robust estimator: the score of Lemma 3 of Chernozhukov et al. (2026), plus the influence of the conditioning share for the ATT and the ATC. None under the plug-in estimator, whose curve no derivation in a source this package cites gives (docs/roadmap.md F26).
psi_max_biasndarray or None: Influence curve of max_bias, as in Theorem 4 of the same paper, so the bias-adjusted bounds get confidence limits rather than being treated as known constants. None under the plug-in estimator or when max_bias is zero.
riesz_representerndarray: (n,) values of \(\\alpha(A, W)\) for the targeted functional.
nu2_estimatorstr: Which estimator of nu2 produced these values.

Methods#

SensitivityElements.psi_nu2: ndarray[tuple[Any, ...], dtype[float64]] | None#

SensitivityElements.psi_max_bias: ndarray[tuple[Any, ...], dtype[float64]] | None#

SensitivityElements.riesz_representer: ndarray[tuple[Any, ...], dtype[float64]]#