26 problems

Randomness conjecture for Ripley's statistic. For squarefree $nneq 7\bmod 8$,

The proposed spatio-temporal model uses an increasing number of spatial basis functions, and its estimated temporal range can become overestimated, which harms predictive performan…

Consider a finite set of spatial locations and a model whose covariance structure is given by a parsimonious Matérn covariance structure. Finite-location identifiability conjecture…

Matheron's characterization conjecture. Matheron's inequalities are not only necessary but also sufficient to characterize a first-order stationary indicator variogram.

Localization conjecture. In many practical settings, this behavior is confined to small regions of the spatial domain and therefore has minimal impact on the overall computation.

Maullin-Sapey implication conjecture. Assumptions 2.2.3a--c of MaullinSapey2022 imply $\widetilde{\textbf{C1}}$, and hence $\widetilde{\textbf{C1}}$ is the weaker assumption.

Continuity-removal conjecture. The continuity assumption on $\gamma$ may be removable by using confinements.

Let the spatial domain be a subset of $\mathbb R^d$, and consider generalized least squares using an undersmoothed working covariance class of fixed smoothness. Let $\beta$ denote…

Let $X$ and $W$ be spatial Gaussian random fields on ${ R} ^d$ with smoothness parameters $\nu_X$, $\nu_W$, and cross-smoothness parameter $\nu_{XW}$. Assume that $\nu_X$ is not a…

Let $X$ be an exposure process, $W$ an unmeasured spatial confounder, and $Y$ a response whose regression slope on $X$ is $\beta$. Say that $W$ is smoother than $X$ when its smooth…

Let $g(\mathbf{s})$ be the spatial process constructed on a finite lattice, and suppose that its idealized infinite-lattice variance is $\mathbb{Z}^2$-periodic. In real application…

Let $\beta$ be the regression parameter in the candidate model, and let $\hat{\beta}_n$ denote its maximum likelihood estimator based on $n$ point observations. Suppose that $[?]$…

Let $u_n(\bm{s})$ be the integral approximation of the moving average process, and let $\eta_n(h)$ denote the residual tail dependence coefficient of…

The setting is local polynomial regression for spatial data on $\mathbb{R}^d$, with bandwidths chosen for estimating the regression function and its derivatives from spatially depe…

The tapered Matérn and generalized Wendland covariance functions are covariance models whose spectral densities have properties analogous to those of the Matérn covariance function…

Let $\boldsymbol\theta_1$ denote the covariance parameters used in the predictor, and let its maximum likelihood estimator replace $\boldsymbol\theta_1$ in the variance ratio from…

Let $w(\cdot)$ be the underlying spatial process in the Gaussian spatial process model with nugget, and consider estimating it from increasingly dense observations on a finite inte…

Diggle–Milne conjecture. No negative binomial point process can simultaneously be orderly, stationary, and ergodic.

Nearest-spacing convergence conjecture. There exists a non-negative, monotone, continuous function $H$ on $[0,\infty)$, supported away from $0$, such that

Electrostatic energy convergence conjecture. There exists a constant $b>0$ such that

Let $\mathcal{P}$ be an Apollonian gasket and let $\mathcal R\subset\mathbb C$ satisfy $\mu(\mathcal R)>0$. For $T>0$, let $F_{T,\mathcal R}(s)$ denote the pair correlation functio…

Let $Z(\boldsymbol{s}_0)$ be the process value at an unobserved location, let $\widehat{Z}_{n}(\mu,\kappa,\beta_1)$ be the predictor based on $n$ observations, and let…

Let $Z$ be a spatial process with spectral density $f$ satisfying condition (f-cond), let $N_\varepsilon$ be a set of observations approaching the origin, and let $b(r)$ denote the…

Let $Z$ be the process under consideration, let $N_\varepsilon$ be a nonempty set of observations approaching the prediction location, and let $F_\varepsilon$ denote the additional…

Limiting domination number conjecture. As $n\to\infty$, the domination number satisfies