We review and formulate results concerning log-concavity and strong-log-concavity in both
discrete and continuous settings. We show how preservation of log-concavity and strongly …

In recent years, log-concave density estimation via maximum likelihood estimation has
emerged as a fascinating alternative to traditional nonparametric smoothing techniques …

Over the last decade or so, Approximate Message Passing (AMP) algorithms have become
extremely popular in various structured high-dimensional statistical problems. Although the …

Supplementary material of “Inconsistency of Bayesian Inference for Misspecified Linear
Models, and a Proposal for Repairing It”. In this paper, we described a problem for Bayesian …

The Wasserstein distance is an attractive tool for data analysis but statistical inference is
hindered by the lack of distributional limits. To overcome this obstacle, for probability …

Adaptive transfer learning Page 1 The Annals of Statistics 2021, Vol. 49, No. 6, 3618–3649
https://doi.org/10.1214/21-AOS2102 © Institute of Mathematical Statistics, 2021 ADAPTIVE …

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 …

Global rates of convergence in log-concave density estimation Page 1 The Annals of Statistics
2016, Vol. 44, No. 6, 2756–2779 DOI: 10.1214/16-AOS1480 © Institute of Mathematical Statistics …

We study generalized additive models, with shape restrictions (eg monotonicity, convexity
and concavity) imposed on each component of the additive prediction function. We show …

Convex regression is concerned with computing the best fit of a convex function to a data set
of n observations in which the independent variable is (possibly) multidimensional. Such …