6 problems

Let $s$ and $K$ be the parameters appearing in the tail-decay upper bound, and let the bound involve the factor $\log(s+K)$. Tail-decay bias conjecture. Theorem is not tight with t…

Let $T$ denote the observation horizon, let $d$ be the spatial dimension, and consider the upper bounds for the squared relative risk of the estimator $\hat{\sigma}^2_*$ of…

Let $\theta^*\in\mathbb{R}^n$ be a signal satisfying the minimum length condition, and let nearly-isotonic regression denote the corresponding constrained estimator with tuning par…

In the equally spaced sequence formulation of concave regression, let $K_n$ be the cone of concave sequences in ${\mathbb R}^n$, let $\hat{\theta}$ be the least-squares estimator o…

Let $\hat{\boldsymbol{\beta}}_{l_0}(\gamma_0)$ and $\hat{\boldsymbol{\beta}}_{l_1}(\gamma_1)$ be the $l_0$ and $l_1$ penalized regression estimators, respectively, with tuning para…

The paper studies risk bounds for the least-squares estimator of a univariate convex regression function, including Theorems and. In the adaptive bound, the relevant logarithmic fa…