Open Access
Translator Disclaimer
2022 Stacked Grenander and rearrangement estimators of a discrete distribution
Vladimir Pastukhov
Author Affiliations +
Electron. J. Statist. 16(2): 4247-4274 (2022). DOI: 10.1214/22-EJS2045


In this paper we consider the stacking of isotonic regression and the method of rearrangement with the empirical estimator to estimate a discrete distribution with an infinite support. The estimators are proved to be strongly consistent with n-rate of convergence. We obtain the asymptotic distributions of the estimators and construct the asymptotically correct conservative global confidence bands. We show that stacked Grenander estimator outperforms the stacked rearrangement estimator. The new estimators behave well even for small sized data sets and provide a trade-off between goodness-of-fit and shape constraints.

Funding Statement

This work was partially supported by the Wallenberg AI, Autonomous Systems and Software Program (WASP) funded by the Knut and Alice Wallenberg Foundataion.


Download Citation

Vladimir Pastukhov. "Stacked Grenander and rearrangement estimators of a discrete distribution." Electron. J. Statist. 16 (2) 4247 - 4274, 2022.


Received: 1 August 2021; Published: 2022
First available in Project Euclid: 17 August 2022

arXiv: 2106.00560
Digital Object Identifier: 10.1214/22-EJS2045

Primary: 62E20 , 62G07 , 62G20

Keywords: constrained inference , cross-validation , discrete distribution , Grenander estimator , isotonic regression , model stacking , rearrangement , smoothing


Vol.16 • No. 2 • 2022
Back to Top