3 problems

Let $p=p_{i\in\mathbb{N}}$ be any distribution on $\mathbb{N}$, let $\tilde p$ be an arbitrary estimator based on $n$ observations, and let $V^*(p)$ denote the population variance-…

Let $p=p_{i\in\mathbb{N}}$ be a distribution over $\mathbb{N}$, let $\hat p$ be its maximum-likelihood estimator, and define … Write $V^*$ and $\hat V^*$ for the corresponding popu…

Consider a scalar Gaussian system or a linear mixing system with a scalar or discrete channel, where the input ${\bf x}$ is sparse Gaussian or mixture Gaussian. Let…