5 problems

Let $X_1,\ldots,X_n$ be independent and uniformly distributed on the sphere $\mathbb{S}^d$, let $\varepsilon_1,\ldots,\varepsilon_n$ be independent standard Gaussian variables inde…

Let $M$ be a compact Riemannian manifold, and consider non-parametric regression on $M$ together with the corresponding Gaussian white noise experiment. The manifold extension conj…

Let $\widehat{\textnormal{dCRT}}$ denote the estimated double conditional randomization test and let $\widehat{\textnormal{MX(2)}}$ denote the resampling-free test obtained by esti…

Consider the reversed two-stage procedure in which eligible units are first matched into groups of size $k'$, their centroids are then matched into homogeneous groups of size $k$,…

Failure of asymptotic equivalence for small $H$. For sufficiently small $H$, asymptotic equivalence between the regression experiments will not hold.