11 problems

Let a discrete distribution's support be partitioned into three subsets: unseen symbols, symbols observed with small frequencies, and high-frequency symbols. Partition-based entrop…

Let $H_S(\underline{\theta})$ denote the selected entropy in the statistical model considered in the paper, and let an estimator be a statistic whose expectation is defined under t…

Sample-complexity conjecture. The sample complexity of constant-space additive-$\epsilon$ entropy estimation is optimal up to factors polynomial in $\log(1/\epsilon)$; in particula…

Conjecture on higher-order CDOTC probabilities. The slower convergence observed for larger $m$ may be caused by the fact that, when $m$ is larger, the probabilities in the correspo…

Let $f$ be a density with finite differential entropy $H(f)$, and consider a partitioning-based estimate of differential entropy whose corresponding partition is deterministic. Det…

Let $k$ be the fixed number of nearest neighbours used in the conventional $k$-nearest-neighbour estimator of Shannon entropy, and let $m\geq 1$ be the dimension. The asymptotic va…

Consider a data-driven plug-in entropy estimate whose estimated support is restricted by design parameters. Complexity–approximation trade-off conjecture. This approach should prov…

Let $\left\{\mu_n:n\geq 0\right\}$ be a random sequence of distributions driven by the classical empirical process and let $\mu$ be the target distribution. Entropy-convergence con…

The estimator $chat{G}_{\textrm{s}}(chat{\theta}_n)$ is constructed by splitting the samples into independent estimators $chat{\theta}_n^{(1)}$ and $chat{\theta}_n^{(2)}$, and appl…

Let $n$ denote the sample size, let $MSE(\text{entropy estimator})$ denote the mean squared error of an entropy estimator, and let $b$ be the corresponding exponent. Conjecture. Fo…

Let $\mathbf{\hat{d}}_j$ and $\mathbf{\hat{d}}$ be the jackknife and original estimators, respectively, and let $\mathbf{\tilde{d}}$ denote the improved estimator. The estimators a…