26 problems

The procedure uses randomly weighted sums of centered estimated vectors $\widehat{\mathbf U}_{j,t}$ to approximate the distribution of the leading term in the debiasing decompositi…

Consider the high-dimensional global testing procedures developed in the paper, including tests based on studentized $L_q$-norm statistics and their monotonically indexed U-statist…

Near-optimality conjecture. This bound is conjectured to be near-optimal when $\Sigma_W$ is unrestricted.

Let $X(1),\ldots,X(N)$ be an i.i.d. sample, and let $\widehat H_i$, $i=1,\ldots,M$, be a permutation bootstrap sample of the estimator $\widehat H(j_1,j_2)$. Let the scales $j_1$,…

In the binary case, let $t(\bx,\by)$ be a statistic that depends only on the response vector $\by$. Write $\hthe_a$ and $\hthe_b$ for the corresponding labeled-data and prediction-…

Let $t(\bx,\by)$ be a statistic that depends only on the response vector $\by$. Write $\hthe_a$ and $\hthe_b$ for the corresponding labeled-data and prediction-powered estimates, r…

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.…

Let $\Delta_\text{gap}$ denote the adjoint gap and let $\mu$ be the parameter approaching zero. We thus conjecture that the adjoint gap $\Delta_\text{gap}$ has a non-analytic behav…

The circular block-maxima method and the disjoint block-maxima method are considered under a suitable triangular-array structure. Variance-advantage conjecture. The advantages of t…

Let $u_2(X)$ denote the toy U-statistic considered in the paper, and let general U-statistics be formed from high-dimensional data. The bootstrap estimates discussed in the paper c…

Convergence conjecture. The lower and upper bounds on spin correlators obtained from $BS_2'$ should converge to each other as the hierarchy level increases when there is a single p…

The kernel-based density-weighted average derivative estimator is studied under small bandwidth asymptotics, with bootstrap-based inference procedures considered through the nonpar…

Let the sample $\mathbf{y}$ consist of elements that can be uniquely ordered, and let the quantile $q\in(0,1)$ be fixed. Let $\psi$ denote the index of the original order statistic…

The stationary bootstrap constructs replicated series by concatenating consecutive blocks sampled from the observed series, and the prediction procedure uses the final $m$ observat…

Random-weight bagged posterior conjecture. The bagged posterior Bernstein–von Mises theorem stated earlier should also hold for these independent nonnegative random weights.

Let $n=1{,}000$ be the sample size, and let $\mathbf{\tilde {V}}_{n}^{\mathtt{ND}}$ and $\mathbf{\tilde{V}}_{n}^{\mathtt{MS}}$ denote, respectively, the numerical derivative and pl…

In the current status model, let the maximum likelihood estimator be used to generate bootstrap samples by resampling the observed censoring indicators from the fitted model. Point…

The current status model concerns inference for an underlying distribution function based on censored observations, with the Grenander estimator as its nonparametric maximum likeli…

Let $X_1,\ldots,X_n$ and $Y_1,\ldots,Y_n$ be the random vectors and i.i.d. approximating random vectors from Theorem 1, with $S_n$, $\widetilde{S}_n$, $K$, $C_{\mathscr{B}}$,…

In the measurement error model $Y=X+\varepsilon$, let $X$ and $\varepsilon$ be independent real-valued random variables with unknown densities $f_X$ and $f_{\varepsilon}$, and supp…

Let $a$ of the $n$ observations be selected either by subsampling or by the $a$ out of $n$ bootstrap, and consider the corresponding pure forests. Table describes the relevant comp…

Bootstrap failure conjecture. The standard nonparametric bootstrap will also fail to provide valid inference for other alternative asymptotics frameworks.

The CLS framework combines estimators using a proportion parameter, and this parameter need not have a closed-form expression. CLS applicability conjecture. The CLS framework could…

Adaptation conjecture. Subject to appropriate modifications, the suggested basic resampling algorithm can be adapted to different testing problems concerning comparisons of populat…