3 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 $f$ be a density on the sphere, and let $n$ denote the sample size. A bandwidth is non-degenerate if it is strictly positive and minimizes the mean integrated squared error. No…

Let $f$ be a function admitting five derivatives at $0$, let $p_n$ denote the dimension sequence, and let $n$ denote the sample-size sequence. Assume that … Let…