4 problems

Let $X_1,\ldots,X_n$ be i.i.d. random variables with unknown density $s$ with respect to a measure $\nu$ on $(E,\mathcal{E})$. Let $h$ denote the Hellinger distance between densiti…

For $\lambda>0$, consider estimating the qubit-state parameter in the Hellinger-distance asymptotic regime, with the corresponding Poisson limit parameter $\mu=n\lambda$. Minimax-c…

Let a mapping used for dimensionality reduction be noncontractive, meaning that it does not decrease the distances between points. Consider the Hellinger distance on the probabilit…

Let $p_0=h_s\circ\varphi_0\in\mathcal{P}_s$ be the density of an i.i.d. one-dimensional sample, and let $\widehat p_n=h_s(\widehat\varphi_n)$ be its $s$-concave maximum likelihood…