6 problems

Compound Poisson representation conjecture. Analogous compound Poisson representations may hold for the class of alpha-stable Poisson-Kingman sampling models.

Let $S$ be a compound Poisson process with Pareto($\alpha$) step sizes, where $\alpha>3$, and consider the convergence in the paper's asymptotic result with $m_n=n$. In this settin…

Let $K_n$ denote the true model dimension, and let $n$ be the sample size. Suppose the posterior contracts at rate $K_n/n$ under the compound Poisson prior, while the maximum likel…

The paper considers estimation of the Lévy measure of a discretely observed compound Poisson process, with the spectral approach based on the representation of the Lévy measure thr…

Nickl–Reiß conjecture. In this discretely observed setting, it should be possible to develop a result similar to Donsker's theorem for inference on the jump distribution $F$.

Exponential-order conjecture. The orders on the right-hand side, respectively, are the correct ones; namely, in the uniform $[0,1]^d$ case and the uniform Cantor-set case, the disp…