14 problems

Let $F_0$ have a continuous positive density $f_0$ on $(0,M)$, where $M>0$, and let $t_0\to(a,b)$ be an interior point. Let $\hat F_n$ be the nonparametric maximum likelihood estim…

Deconvolution conjecture. A conjecture on deconvolution is raised that would permit completing the proposed theory.

Equal-rate convergence conjecture. The rate of convergence of $|R^{\star}-\widehat{R}|$ is the same when the density $f^{\star}$ is known and when it is unknown.

Impossibility conjecture. There is a regime in which $f$ cannot be estimated consistently when $t>\frac{3}{2}d$.

Let $\kappa\in(0,1)$, and let $(P_K)_{K\geqslant0}$ be the orthonormal polynomials for the scalar product … with $\deg(P_K)=K$, where $h_\kappa$ is the probability density defined…

Let $\kappa\in(0,1)$, and let $(P_K)_{K\geqslant0}$ be the orthonormal polynomials for the scalar product … with $\deg(P_K)=K$, where $h_\kappa$ is the probability density defined…

Partition-negligibility conjecture. There is at least one partition such that

In the measurement error model $Y=X+\varepsilon$, let $X$ and $\varepsilon$ be independent real-valued random variables with unknown densities $f_X$ and $f_{\varepsilon}$, and supp…

Let $W_p$ denote the Wasserstein distance of order $p$, and consider the deconvolution model and tail conditions assumed in Theorem … are appropriate under the assumed tail conditi…

In deconvolution, an estimator for the distribution function can be obtained by integrating a density deconvolution estimator, with a truncation of the integral used to perform an…

Let $d=1$, let the error distribution belong to a class of ordinary-smooth error distributions of order $\beta$, and measure the integrated deconvolution risk through the Wasserste…

Consider pointwise estimation of a cumulative distribution function when the unknown density is $m$ times differentiable and the error distribution is ordinary smooth. Fan's conjec…

Groeneboom's deconvolution local limit conjecture. For the estimator $F_n^{(1)}$ appearing in the decreasing-mixture deconvolution model,

Improved-rate estimator conjecture. The estimator $(\hat M,\hat G)$ minimizing