7 problems

Variance bound conjecture. The variance of the estimator is upper-bounded by an expression of order

The Large Outliers setting refers to simulations in which the outcome distribution includes high-degree nodes with large outcomes. The relevant variance estimator is denoted by…

Small-friction derivative estimate. It is conjectured that

Let $\widehat{C}_{\mathrm{jump}}$ be the jump-based estimator of the minimal-penalty constant, constructed from a collection of candidate estimators. Jump-estimator variance conjec…

Suppose that the observed data follow the Gaussian linear model … where $\boldsymbol{\beta}\in\mathbb{R}^d$ is an unknown, potentially dense signal, the rows of $X$ are independent…

Variance estimation and adaptive shrinkage conjecture. Even if $\boldsymbol{\beta}$ does not satisfy any sparsity conditions, it may be possible to effectively estimate $\sigma^2$…

Let $\Gamma_n^2(h)$ be the kernel estimator of the asymptotic variance associated with the function $h$, let $G_{\theta_{k-1}}(X_{k-1},X_k)$ be the corresponding martingale increme…