A selection of published work on the Pivotal Information Criterion
(PIC) and the methods implemented in picreg.
The Pivotal Information Criterion
Sardy, van Cutsem & van de Geer (2026). arXiv:2603.04172
The companion paper that introduces PIC. It develops the pivotal detection-boundary principle and the (asymptotic) pivotality of the null gradient statistic, then studies support recovery and the phase-transition behavior empirically, benchmarking PIC against competing methods on real-world datasets.
A pivotal transform for the high-dimensional location-scale model
van de Geer, Sardy & van Cutsem (2025). arXiv:2512.18705
The theoretical backbone of PIC in the location-scale setting: the exponential transformation of the log-likelihood whose \ell_1-penalty tuning parameter does not depend on the unknown scale parameter, generalizing the square-root Lasso beyond quadratic loss. The tuning parameter can asymptotically be taken at the detection edge, and the paper proves an oracle inequality, variable-selection consistency, and asymptotic efficiency of the scale and intercept estimators, with examples including the Subbotin and Gumbel distributions.