17 problems

Let ${\mathbb D}_\beta$ denote the limiting distribution associated with the flatness parameter $\beta$, for $0<\beta<\infty$. Consider Brownian motion with no drift, corresponding…

Data augmented bootstrap (DAB) uses Euclidean structures, the Kolmogorov metric, and Gaussian universality to obtain coverage guarantees through distributional approximation. Non-E…

Data augmented bootstrap (DAB) constructs confidence intervals using approximate invariance, with validity based on distributional approximation between suitably chosen statistics.…

Uniform asymptotic exactness conjecture. For every $\alpha\in(0,1)$, there is no confidence set that is asymptotically exact uniformly over $\mathfrak{Ber}$ at level $1-\alpha$.

Asymptotic behavior conjecture. The situation for $r=3$ and $\gamma=1.5$ should be similar to that for $\gamma=0.5$, although much larger sample sizes may be needed to observe this…

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…

Consider the positivity-constrained Gaussian inverse problem … where $\bK\in\mathbb{R}^{m\times p}$ is a forward linear operator, not necessarily of full column rank, and let…

Let $C_0^{M\infty}$ be the two-sided confidence interval constructed in the paper. Say that $C_0^{M\infty}$ has no ties when its defining criterion does not attain tied values. Adm…

The model concerns confidence intervals for a regression coefficient $\theta^*_j$, including exact intervals obtained by inverting tests, leave-one-out confidence intervals, and de…

Reliability conjecture. The constructed confidence interval under the stochastic case is $L_2$-weakly reliable if

Let $f_0$ be the monotone regression function, let $x_0$ be the point of inference, and let $\widehat{f}_n^{-}(x_0)$ be the block max-min estimator with associated block count…

Let $X_1,\dotsc,X_n$ be independent and identically distributed random variables, and let $m_\alpha$ be the confidence-bound function defined from the order statistics of a sample…

Guaranteed-coverage conjecture. For every sample size $n\geq 1$, every $\alpha\in[0,1]$, and every distribution supported on $[0,1]$,

Honesty conjecture. For any $M$, the resulting confidence interval is asymptotically honest over the intersection of $\mathcal{F}({M})$ and that appropriately defined set of regres…

Let $f_0$ be a decreasing density on $[0,infty)$, let $X_1,\dots,X_n$ be a sample from $f_0$, and let $\hat f_n$ be the Grenander estimator, defined as the left derivative of the l…

Consider Ma's empirical Bayes confidence interval, modified by replacing its empirical Bayes point estimator with a hierarchical Bayes-type point estimator. Let $\alpha$ denote the…

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…