5 problems

Let $Y\sim {\rm N}_d(\theta,N^{-1}I_d)$, with the mean vector split into disjoint blocks $\theta^{(1)},\dots,\theta^{(B)}$ of sizes $d_1,\dots,d_B$, where $d_1+\dots+d_B=d$. Define…

Horseshoe nonactive-contraction conjecture. Because this horseshoe choice satisfies the lower-bound condition on $\tau$ but not the upper-bound condition, the horseshoe prior shoul…

In the normal sequence model, let $t=\{2\log(n/s)\}^{1/2}$ be the hard-thresholding threshold, and let the polynomially decaying prior have parameters $\tau$ and $\alpha$. Sharp-mi…

Consider estimating the mean vector of a $p$-variate Normal distribution when the covariance matrix is an unknown multiple of the identity. For the class of generalized prior distr…

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