Estimate the corrupted signal strength in a model with (sub-)Gaussian covariates
sloe(object)A scalar.
an "mdyplFit" object.
Ioannis Kosmidis [aut, cre] ioannis.kosmidis@warwick.ac.uk
The Signal Strength Leave-One-Out Estimator (SLOE) is defined in
Yadlowsky et al. (2021) when the model is estimated using maximum
likelihood (i.e. when object$alpha = 1; see mdyplControl() for
what alpha is). The SLOE adaptation when estimation is through
maximum Diaconis-Ylvisaker prior penalized likelihood
(mdypl_fit()) has been put forward in Sterzinger & Kosmidis
(2025).
In particular, sloe() computes an estimate of the corrupted
signal strength which is the limit $$\nu^2$$ of \(var(X
\hat\beta(\alpha))\), where \(\hat\beta(\alpha)\) is the maximum
Diaconis-Ylvisaker prior penalized likelihood (MDYPL) estimator as
computed by mdyplFit() with shrinkage parameter \(alpha\).
Sterzinger P, Kosmidis I (2024). Diaconis-Ylvisaker prior penalized likelihood for \(p/n \to \kappa \in (0,1)\) logistic regression. arXiv:2311.07419v2, https://arxiv.org/abs/2311.07419.
Yadlowsky S, Yun T, McLean C Y, D' Amour A (2021). SLOE: A Faster Method for Statistical Inference in High-Dimensional Logistic Regression. In M Ranzato, A Beygelzimer, Y Dauphin, P Liang, J W Vaughan (eds.), Advances in Neural Information Processing Systems, 34, 29517–29528. Curran Associates, Inc. https://proceedings.neurips.cc/paper_files/paper/2021/file/f6c2a0c4b566bc99d596e58638e342b0-Paper.pdf.
summary.mdyplFit()