43 problems

Piecewise Convex Information Criterion conjecture. PCIC consistently selects the number of convexity change points and is asymptotically efficient within the class of methods that…

Sharper-threshold conjecture. More accurate bounds for $\lambda_1$ and $\lambda_2$ can be obtained, for example, using techniques from the cited literature.

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 data consist of a highly dependent time series with change-points, and the proposed algorithm estimates both the number and locations of the change-points without relying on ra…

Laplace detection-threshold conjecture. The parameter ranges considered in the experiments lie in the regime $n\gtrsim\sqrt{p}$, where the term $\kappa\propto p^{0.25}n^{-0.5}$ dom…

Multivariate constant-delay conjecture. This strong-signal regime corresponds to Regime 4 in the univariate setting, where the detection delay is also of constant order up to logar…

Heavy-tailed detection-delay conjecture. This slower decay rate reflects the increased difficulty of robust detection under heavy-tailed distributions. The conjecture is motivated…

Let $\varepsilon_i(0)$ and $\varepsilon_i(1)$ denote the potential-outcome errors, and let $\hat\imath_\text{SSE}$ and $\hat\jmath_\text{SSE}$ be the split location and covariate s…

Let $\bm\delta$ be the differential regression parameter and let $\bm\Sigma$ be the covariance matrix. Define … The authors also consider…

Let $G_n$ be a preferential attachment random graph of size $n$, and suppose its affine attachment parameter changes from $\delta_0$ to $\delta_1$ at the late change-point … where…

Let $x$, $y$, and $z$ be three points on the real line, where $x$ and $z$ are generated independently from two distinct distributions and $y$ is generated from their 50--50 mixture…

Let $X$ and $Z$ be independent draws from arbitrary unknown probability distributions with densities $f_X$ and $f_Z$, satisfying … Let $Y$ be drawn from the mixture distribution ……

Let an $\ell_0$-penalised method penalise the number of change points in a piecewise-constant mean estimation problem, while an $\ell_1$-penalised method penalises their magnitudes…

Powerlessness conjecture. When $\gamma<\tfrac{1}{2}$, all tests based on the vertex degrees $\{D_v(n)\}_{v\in[n]}$ are powerless, and all tests based on $G_n$ are powerless.

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…

Necessity conjecture. The stronger condition above is necessary for the inference tasks, specifically for establishing uniform tightness of the refined change point estimators in t…

Consider the simple linear regression change-point model with independent, zero-mean normal errors, and let $W$ be the maximum likelihood ratio statistic … where … with…

Let a time-series spectrum exhibit either a break or a smooth change of the form discussed above simultaneously at multiple frequencies. Multiple-frequency pooling conjecture. The…

The paper studies change point detection under a dynamic Huber $\varepsilon$-contamination model, where contamination distributions may differ at each observation. Its scanning-win…

Consider a change-point $\tau_k$ with associated scale $r_k$, effective height $\bar\Delta_k$, and critical height function $\rho^*_{r_k}(\cdot)$. Conjectured detection threshold.…

Fix an even range $r\geq 2$, and suppose that $n/(2r)$ is an integer. Let $\rho^*_{r}(\cdot)$ denote the critical height function, and let $({\bf NoSp})$ and $({\bf Detect})$ denot…

Sobolev rate conjecture. The detection boundary should be of order

Signal-to-noise gap conjecture. This gap is caused by a loose upper bound, which in turn is caused by insufficiently sharp control of certain cross terms.