70 problems

Steel's conjecture. In the Ising model, in the Kesten–Stigum regime, high-probability tree model estimation may be achieved with $k=O(\log n)$ samples.

Rate-optimality conjecture. Choosing

Consider a one-parameter model with data-generating distribution $P$ and model parameter $\mu^*$, and let an in-model estimator be used to construct a prequential model. In-model r…

Let $(\beta)_{1-\tau_A}$ be the population version of the transformed generator, where $\tau_A$ is the Kendall-type parameter associated with the Pickands dependence function, and…

Ma et al.'s conjecture. If the MLE satisfies the asymptotic normality condition, then the estimation problem is super-teachable.

Misspecified Cramér–Rao bound conjecture. The mean-square error satisfies

Let $f$ be a statistic, let $\mathbf{x}$ be an observation, and let $\kappa(f,\mathbf{x})$ be its structural capacity. Let $C(f)$ denote the single-evaluation variance, and let…

Spectral estimation conjecture. The critical dimension for estimation is conjectured to be

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 $M$ be a smooth manifold with metric $g$, and let $\hat M$ be an estimated manifold with metric $\hat g$. Weighted-Laplacian stability conjecture. Crude stability results for t…

Let $M$ be an unknown sufficiently smooth $d$-dimensional submanifold of $\mathbb{R}^D$. Aamari and Levrard's chart-based manifold estimators can be adapted to construct an estimat…

Let the MLE be the maximum likelihood estimator for multivariate mixtures of power series distributions with a conditional independence structure, and let $\ell_p$ denote the relev…

Let the maximum likelihood estimator (MLE) be used for the local Poisson deconvolution model with a Gaussian kernel. Let the regime $m\to\infty$ denote the asymptotic regime in whi…

Let $\mathscr{L}$ be a rich loss space, for example the space of all continuous losses satisfying mild growth conditions, and let optimality be defined by a natural optimality noti…

Let $\mu$ be a distribution on $\mathbb{R}$, and consider estimators for the associated location family. An estimator is shift-invariant if shifting every observation by $c$ shifts…

Let $\mu$ be a distribution on $\mathbb{R}$, and let an $n$-sample estimator be a function of observations from the corresponding location family. For a fixed tolerance $\delta$, i…

Let a distribution on a compact space be given, and consider estimators evaluated by their worst-case probability of estimating the parameter within a prescribed tolerance. An esti…

One-sided estimation lower-bound conjecture. There exist constants $c_0,c,r>0$ such that, for every $s,n\in\mathbb{N}$ satisfying

Consider the degree-corrected mixed membership model with probability matrix $\boldsymbol{P}$, membership-related matrix $\boldsymbol{G}$, and first singular vector…

In a degree-corrected mixed membership model, let $\theta_i$ denote the degree parameter of node $i$, let $\boldsymbol{\Theta}$ denote the degree-parameter vector, let…

The discussion concerns estimators whose precise statistical setup is not specified in the source excerpt. The claim is that these estimators must be linear. Linearity conjecture.…

Theorem … concern convergence results for point process learning and Takacs–Fiksel estimation under boundedness assumptions. Boundedness-conditions conjecture. Both theorems can be…

Impossibility conjecture. There is no reasonable estimator such that

In the Gaussian geometric planted matching setting, let the signal-to-noise ratio be $\frac{d}{\log n\,\sigma^2}$, and consider the greedy inner-product algorithm studied in the ci…

Consider the Gaussian model with $X_1,\dots,X_n\stackrel{\mathrm{iid}}{\sim}\mathcal{N}(0,I_d)$ and $Z_1,\dots,Z_n\stackrel{\mathrm{iid}}{\sim}\mathcal{N}(0,\sigma^2I_d)$, and let…