15 problems

Adaptive-rate conjecture. A result similar to the established bound

Adaptive minimax optimality conjecture. The convergence rate of the SOLIT rule should be adaptively minimax optimal over the whole range of smoothness classes specified by the inde…

The covariance matrix … , but its privacy term incurs a logarithmic-factor loss. Unavoidability conjecture. This logarithmic loss is unavoidable for adaptive estimation under diffe…

Let an adaptive iterated KRAS estimator be an iterated Tikhonov KRAS estimator whose regularization or stopping choice is selected adaptively, as in the adaptive LRAS procedure dis…

Let $F$ be a property of a distribution $p$, let $p^{\mathrm{PML}}$ denote the profile maximum likelihood distribution, and suppose the PML error bound has amplification factor…

Unconditional lower-bound conjecture. Theorem 1 should remain valid without this assumption. The assumption is used to obtain lower bounds for adaptive estimators based on reasonab…

Let $n$ be the sample size, let $\varepsilon$ denote the estimation accuracy, and let PML denote the profile maximum likelihood approach to adaptive property estimation. PML optima…

Adaptation conjecture. Adaptation to the unknown noise variance $\varepsilon^2$ can be achieved without loss of the estimation rate in the sparse zone $s\le \sqrt{d}$. In the prese…

The paper considers estimation of the Lévy measure of a discretely observed compound Poisson process, with the spectral approach based on the representation of the Lévy measure thr…

Pointwise-selection impossibility conjecture. Constructing an optimally adaptive estimator for all values of the nuisance parameters via pointwise selection is impossible; other me…

Negative adaptation conjecture. Adaptation does not occur when the support $\Omega$ is a general convex body and the regression function is polyhedral, within the current methods b…

Higher-dimensional logarithmic-loss conjecture. The logarithmic loss due to adaptation is unavoidable also when $d>1$.

Let $\tau$ and $C$ be unknown parameters in the Pareto model described above, and let the adaptive and uniform confidence intervals for $\tau$ have upper bounds differing from the…

Minimax-rate conjecture. The presented lower bound is correct, and consequently the upper-bound result should be improved. The critical case $(2\beta+1)p=r$ is the only case in whi…

In a single-index regression, the linearity condition is the condition under which the conditional mean of the covariates given the index is linear in the index, and an adaptive es…