Papers › Diaconis-Ylvisaker prior penalized likelihood for p/n →κ∈(0,1) logistic regression
Diaconis-Ylvisaker prior penalized likelihood for p/n →κ∈(0,1) logistic regression
Philipp Sterzinger, Ioannis Kosmidis
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
We characterise the behavior of the maximum Diaconis--Ylvisaker prior penalized likelihood estimator in high-dimensional logistic regression, where the number of covariates is a fraction κ∈(0,1) of the number of observations n, as n →∞. We construct a rescaled estimator with zero asymptotic aggregate bias and define adjusted Z-statistics and rescaled penalized likelihood ratio statistics that exhibit the typical null asymptotic distributions, when the covariates are independent multivariate normal with an arbitrary covariance matrix and the linear predictor has asymptotic variance γ². While the maximum likelihood estimate asymptotically exists only for a narrow range of (κ, γ) values, the maximum Diaconis--Ylvisaker prior penalized likelihood estimate always exists and can be computed directly using standard maximum likelihood routines. Thus, our asymptotic results extend to (κ, γ) values where the maximum likelihood framework breaks down, with no additional implementation or computational cost. We study the estimator's shrinkage properties, compare the proposed estimation and inference procedures with alternatives that also accommodate proportional asymptotics, and formulate a conjecture -- supported by strong empirical evidence -- that extends our results when the model includes an intercept parameter. Finally, we propose estimation methods for all unknown constants involved in our procedures and demonstrate the theoretical advances through extensive simulation studies and the analysis of digit recognition data.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections