3 problems

Sharp upper-bound conjecture. The lower bound may be loose, while the upper bound may be sharp. The bounds coincide for $\ep\leq n^{-(s+2)/(2s+1)}$ and otherwise leave a gap whose…

Let $X$ be a sample from the uniform location estimation problem, let $\theta$ denote the location parameter, and let $\hat\theta_k(X)$ be an estimator indexed by $k$. Write…

Consider the Gaussian linear regression model with $X\sim \mathcal{N}(0,\sigma^2 I_p)$ and $Y=X^T\beta+z$, where $z\sim \mathcal{N}(0,1)$ is independent of $X$. Let the true parame…