7 problems

Let $X$ be a random variable supported on a set $A\subset \mathbb{S}^m$ whose convex closure has nonzero volume and which has a unique Fréchet mean $\mu$. A point $\mu$ is Type I f…

Let $X$ be a random variable supported on a set $A \subset \mathbb{S}^m$ whose convex closure has nonzero volume and which has a unique mean $\mu$. A point $\mu$ is Type I finite s…

Let $X$ be a compact metric space, and consider random variables taking values in $X$ whose Fréchet means and sample Fréchet means are defined. A distribution is smeary when its Fr…

Let $X$ be a random variable on a metric space. A distribution is smeary when its Fréchet mean has a limiting convergence rate slower than the classical $n^{-1/2}$ rate, and it has…

Let $X$ be a random variable on $\mathbb{S}^m$ whose local Fréchet mean is smeary, as in the curse of dimensionality theorem, and let the corresponding local Fréchet means be those…

Let $m\geq 2$, and let $F$ and $G$ denote the Fréchet functions associated with the intrinsic and comparison distance settings, respectively, near the origin $0$ in the real projec…

Let $\mathcal H$ be the underlying Hilbert space, and let $\Sigma_1,\dots,\Sigma_n$ be covariance operators on $\mathcal H$. Assume that $\Sigma_1$ is injective, and let…