This book treats the latest developments in the theory of order-restricted inference, with
special attention to nonparametric methods and algorithmic aspects. Among the topics …

Summary Let X 1,…, X n be independent and identically distributed random vectors with a
(Lebesgue) density f. We first prove that, with probability 1, there is a unique log-concave …

The divide and conquer method is a common strategy for handling massive data. In this
article, we study the divide and conquer method for cubic-rate estimators under the massive …

Divide and conquer in nonstandard problems and the super-efficiency phenomenon Page 1
The Annals of Statistics 2019, Vol. 47, No. 2, 720–757 https://doi.org/10.1214/17-AOS1633 © …

A review of uncertainty quantification for density estimation Page 1 Statistics Surveys Vol. 15
(2021) 1–71 ISSN: 1935-7516 https://doi.org/10.1214/21-SS130 A review of uncertainty …

The goal of this paper is to study the bootstrap for the Grenander estimator. The first result is
a proof of the inconsistency of the nonparametric bootstrap for the Grenander estimator at a …

We aim at estimating a function λ: 0, 1→ ℝ, subject to the constraint that it is decreasing (or
increasing). We provide a unified approach for studying the L_p-loss of an estimator defined …

The limit distribution of the Linfty-error of Grenander-type estimators Page 1 The Annals of
Statistics 2012, Vol. 40, No. 3, 1578–1608 DOI: 10.1214/12-AOS1015 © Institute of …

Limit distribution theory for block estimators in multiple isotonic regression Page 1 The
Annals of Statistics 2020, Vol. 48, No. 6, 3251–3282 https://doi.org/10.1214/19-AOS1928 © …

This paper is about optimal estimation of the additive components of a nonparametric,
additive isotone regression model. It is shown that asymptotically up to first order, each …