57 problems

Careless responding refers to answering survey items without basing responses on their content. Ward et al.'s conjecture. Careless responding is likely present in all survey data.…

Let $P$ be a set of $n$ points, and let regression depth be the minimum number of points intersected by a hyperplane during any continuous motion taking it to a vertical hyperplane…

Let $\widehat{\bm{S}}_n$ be the normal-scores covariance and let $\widehat{\bm{\Sigma}}^{\tau}$ be the sin-transformed Kendall matrix. Assume $p/n\to\gamma$. Spectral equivalence o…

Laplace detection-threshold conjecture. The parameter ranges considered in the experiments lie in the regime $n\gtrsim\sqrt{p}$, where the term $\kappa\propto p^{0.25}n^{-0.5}$ dom…

Heavy-tailed detection-delay conjecture. This slower decay rate reflects the increased difficulty of robust detection under heavy-tailed distributions. The conjecture is motivated…

In the unknown-variance setting, let $\epsmax$ denote the maximum contamination proportion, and consider the regimes in which $\epsmax>1/3$ and $\epsmax>7/15$, where the lower-boun…

Let TME and LNSMI denote the existing methods studied in the paper, and consider the observed deterioration in their performance when outliers form clusters, with sample size…

Dimension-free robustness conjecture. The dimension-dependent factor in the lower bound of Theorem 2.6 is unnecessary; equivalently, the corresponding asymptotic lower-bound expres…

Let $\mu$ be a distribution and let $\mathcal{F}[\mu,\psi]$ denote the relevant concentration objective for a coordinate $\psi$. Given $n$ samples, let $\hat{\psi}_n$ be a data-dri…

Let $\mathcal{P}$ be a distribution family on $(0,\infty)$ whose members have power-law tails satisfying $P(X>x)\sim x^{-\alpha}$ for some $\alpha>0$. Let the logarithmic coordinat…

The breakdown point for a simpler version of regression MM-estimators in a linear mixed-effects model has been discussed, but the exact value is not derived in the source. The exac…

The normalized multivariate Kendall's $\tau$ matrix is the high-dimensional matrix studied in the paper, with its eigenvalues ordered from the spectral analysis of that matrix. Ext…

Let $\lambda_{\texttt{min}}$ denote the minimum visitation probability in the asynchronous Q-learning setting described above. Visitation-probability dependence conjecture. Some de…

The halfspace depth function $HD(t_n x,\mathbb{P}_n)$ can be normalized by a speed of convergence $N(t_n)$ to study its convergence toward $1$, but observing this numerically requi…

Converse conjecture. The Lipschitz logarithmic map condition is valid only if the sectional curvature at $x^*$ is upper bounded.

The result concerns robust mean estimation for data that are both Markovian and adversarially contaminated. In particular, the estimator texttt{RUMEM} achieves, under the stated Hu…

Let $X_1,\ldots,X_n$ be independent and identically distributed according to … where the scale parameter $\sigma$ is unknown. Let $\widehat{\sigma}$ be a robust estimator satisfyin…

Let $S$ be a multiset of samples, let $\boldsymbol{\theta}>0$ and $\boldsymbol{\rho}e 0$, and let $m otin e 0$? A sample set is $(epsilon,delta,m)$-certifiably resilient if there i…

Let $R_n(0)$ denote the set of Tukey medians at the origin for data following an isotropic normal distribution in dimension $d=2$, and let $\operatorname{diam}(R_n(0))$ denote its…

Let $P_X$ be the distribution of observations on a general Riemannian manifold, and let Assumption (A4) denote the regularity conditions used for the central limit theorem of sampl…

Let $F_n^c$ denote the empirical Huber objective for a sample of $n$ observations on a Riemannian manifold. Gradient Lipschitz continuity means that there is a constant $L_c$ such…

Let $k$ be the sparsity parameter and $\beta$ the accuracy parameter in robust sparse mean estimation, and write $\widetilde{\Theta}(k^2/\epsilon^2)$ for sample complexity up to po…

Fixed-sample concentration conjecture. For a given sample size $n$, a concentration inequality of the same type should hold without the $\log(n)$ term.

Sample-complexity conjecture. A tighter lower bound exists for this estimation problem, matching the upper bound of Ramsay et al.

The robust outlier bound condition (ROBC) yields a threshold $s^*$, arising from the analysis of the product of two normal random variables. Tight-threshold conjecture. The conditi…