18 problems

Asymptotic quasi-Bayesian learning conjecture. Results analogous to these posterior-concentration and coverage conditions can be established in the quasi-Bayesian context of the ar…

Let $Q_N^{\dagger}$ denote the increasing rearrangement of the quantile martingale posterior draw $Q_N$, and let $S_N^{\dagger}$ denote the corresponding centered and scaled proces…

Let $C_{\mathcal{G},\bm{\psi},\bm{\ell},Q}$ be a clustered Archimax copula, and let $\mathcal{D}_2$ and $\mathcal{D}_3$ be the classes of clusters specified by the extended max-dom…

Let $\Phi$ be the regression matrix, let $\hat{\eta}_{\operatorname*{EB}}$ be the empirical Bayes hyper-parameter estimator, and let $\eta_{\operatorname*{b}}^{*}$ denote its limit…

Fixed-design validity conjecture. For the fixed design, these theoretical results are still valid under appropriate regularity conditions.

Limiting-distribution conjecture. The limiting distribution of the point estimator under a misspecified exposure mapping can be characterized under weaker conditions than those cur…

Consider the heteroscedastic transformation model discussed in the paper, and let a pretransformation of the response $Y$ by its empirical distribution function $\hat{F}_Y$ be appl…

Let $d_{\mathbf{X}}$ denote the dimension of the covariate vector, and consider the convergence results of the lemmas described in the surrounding discussion, which currently requi…

Eigenvalue asymptotic-normality conjecture. The eigenvalues of $\widehat{\mathbf{R}}^{(i)}$ should be asymptotically normally distributed about the eigenvalues of…

Let $Y$ be a random variable, let $X$ take values in a compact set $\mathcal{X}\subset\mathbb{R}^q$, and let $\beta_0$ be an interior point of a bounded set…

Tan and Zhu's conjecture. The leading term $n^{1/3}$ in the admissible divergent-covariate rate would be close to optimal.

Suppose the value-function estimator $V_N(z,\lambda)$ and the population value function are sufficiently smooth, and let $\lambda$ be the smoothing parameter. The derived rate for…

Doss's localization conjecture. The quantity $E_{n,b}$ is asymptotically negligible for sufficiently large $n$ and $b$. This is intended to justify localization of the likelihood r…

Equivalence conjecture. Both estimators have the same asymptotic properties.

Non-vanishing conjecture. For $N\geq 2$ and $\gamma=1$, $\mathbf{Q}_{n}$ generally does not converge in probability to zero.

Higher-order mismatch conjecture. In general, the higher-order terms of $q(\theta \mid \boldsymbol{D})$ and $p(\theta \mid \hat \theta)$ do not match each other.

LIL approximation conjecture. The LIL $q(\boldsymbol{D} \mid \theta)$ should approximate the density $p(\hat \theta \mid \theta)$ of $\hat \theta$.

Asymptotic equivalence conjecture. If the components $f_{i\ell}$ in have a symmetric distribution, then the asymptotic behaviour of…