24 problems

Let $T$ be a detection procedure, and let $\mathbb{E}_k$ and $\mathbb{E}_{\infty}$ denote expectation when the change occurs at time $k$ and when no change occurs, respectively. De…

The nonparametric Kiefer--Weiss problem considers sequential testing with error probabilities tending to zero, equivalently as $c\to\infty$, where $c$ is the parameter governing th…

The statistics $\mathrm{SeMI}^{\mathrm{Unif}}$, $\mathrm{SeMI}^{\mathrm{max}}$, and $\mathrm{SeMI}^{*}$ are considered in the sequential membership inference setting. The uniform d…

Let $T(j,\alpha_t)$ be the moving boundary used by the textsc{StageSampling} procedure, which adaptively samples at a design point and stops when the accumulated statistic satisfie…

Let $\mathsf{H}_0,\mathsf{H}_1,\dots,\mathsf{H}_N$ be the hypotheses in a general non-i.i.d. stochastic model, and let $\lambda_{ij}(n)$ denote the log-likelihood ratio between…

Asymptotic optimality conjecture. Asymptotic optimality properties hold for this multistream finite moving average detection procedure.

Exponential-order conjecture. The current analysis conjectures that

Consider the proposed sequential change-diagnosis scheme, operating over possible change-points. Uniform error control means that its error probability is bounded by the prescribed…

For a family of constants … let … Here $W_{ij}(n)$ is the relevant CuSum statistic, and $\tau(b,h)$ is the stopping time for threshold parameters $b$ and $h$. Uniform tail-bound co…

Minimax scaling conjecture. The scaling

Dependence-structure conjecture. This conditional-asymptotic approach should be possible if a suitable dependence structure allowing, for example, for big-block-small-block argumen…

Let $u$ denote the change-point time, $theta$ the covertness requirement, and $u$ and $theta$ satisfy the conditions considered for LPD communication under the Shewhart, CUSUM, a…

In a periodic independent, identically distributed model, consider quickest change detection under Lorden's minimax criterion, and allow stopping algorithms whose thresholds vary p…

Consider a non-Bayesian or minimax version of the change-detection problem studied in the paper, and let the false alarm rate vary over its possible values. A single-threshold poli…

The classical Shiryaev formulation compares the periodic-Shiryaev algorithm with the classical Shiryaev algorithm for detecting a change, using false-alarm and delay penalties. Exi…

Third-order asymptotic optimality conjecture. For the Pollak min-max criterion, when $R_t$ is initialized with $r_*=2.299812$, the stopping rule $T_*$ is third-order asymptotically…

Let $f_\lambda(R)$ be the function defined by the integral equation in the paper, let $r_*$ be the positive constant determined by … and let $\lambda\geq 0$. The inequality conject…

Let $K$ sensors monitor for a change, of which at most $M$ may be corrupt. The Low-Sum-CUSUM procedure stops when the sum of the smallest $K-M$ local CUSUM statistics crosses a fix…

The paper considers multiple testing procedures for independent streams of data that control the familywise error probabilities of both types. The procedures are evaluated by their…

Let the virtual arm have mean $(\mu_{1,1}+\mu_{2,1})/2$, where the arms in the first action are denoted by $\mathcal{P}_1$ and the remaining arms are the other arms. Virtual-arm re…

Let $\mathcal{S}_A^r$ denote the Shiryaev–Roberts–$r$ procedure with threshold $A$ and initialization point $r\geq0$. For a false-alarm constraint…

Let $\dot{\delta}_{z}(a)$ denote the geometric sampling procedure whose probability of stopping at the end of each stage is constant across stages, with the stopping probability al…

Information-time conjecture. This simple form of information time is true for most response-adaptive randomization procedures.

Worst-changepoint-at-infinity conjecture. The worst changepoint for the SR-$r$ procedure is at infinity: the supremum of the conditional average detection delay over changepoints i…