8 problems

Let $f(\lambda)=(2\pi)^{-1}|1-e^{i\lambda}|^{2r}$ and let $\mathcal{F}_r(g)$ be the class of spectral densities defined in the source. For each $r\in\mathbb{N}$, consider the BLUE…

Epsilon-relaxation conjecture. Using an $\epsilon$-relaxation is unnecessary in this setting.

Let an experimental design assign treatment indicators with possibly non-uniform first-order probabilities, so that $\boldsymbol{z}$ is not required to satisfy $ui=frac{1}{2}$ for…

The statistical seriation model concerns estimating an unknown seriation structure from noisy data; the least squares estimator achieves statistically optimal rates but requires se…

The CLS framework combines estimators using a proportion parameter, and this parameter need not have a closed-form expression. CLS applicability conjecture. The CLS framework could…

A scalar Lévy channel is a channel whose output conditioned on the input has an infinitely divisible law. The Gaussian and Poisson observation models are the principal examples, an…

Let $X$ be a non-negative random variable input to the scalar Poisson channel, and let $P$ and $Q$ be probability measures governing the input under the true and mismatched models,…

Effective signal-to-noise ratio estimation conjecture. It may be possible to derive effective estimators of $\eta^2$ when $d \geq n$, provided $\sup d/n < \infty$.