6 problems

Near-optimality conjecture. For all $r\in\mathbb{N}$, the $\ell_0$-penalised least-squares method should itself be nearly optimal in both the signal-strength condition and the loca…

Let $Y=\psi_0(\bm\alpha_0^T\bm X)+\varepsilon$, where $\bm X$ is a $d$-dimensional random vector, $\psi_0$ is an unknown monotone link function,…

Let $\hat{\theta}_{\Pi}$ denote the least squares estimator associated with a model or cone indexed by $\Pi$. In the model-selection setting for piecewise monotone signals, one see…

Let y=\theta^*(\boldsymbol{[?])+[?] be observed under the latent-permutation anti-Monge model, and let $\bar{\mathcal{M}}$ denote the unrestricted anti-Monge parameter space. The…

Let $X$ be a covariate vector whose components may be continuous or discrete, and consider the bundled least-squares estimator in the monotone single index model. Mixed-design conv…

Let the true function be non-convex, and let its projection onto the class of convex functions have linear components, called misspecified regions. Let the LSE denote the convex le…