7 problems

Let $F$ be the distribution function of the transformed observations, let $\hat F_n$ be the empirical distribution function based on the rank-based pseudo-observations, and define…

AE-KDE robustness conjecture. AE-KDE's particularly poor performance was due to its robustness: the reconstruction loss was low during the injected time period, causing false-negat…

Covariance operator estimation concerns recovering a covariance operator from observations, while kernel density estimation is studied using Fourier analysis techniques. Fourier-an…

Let $X$ be the sample used to form the min-max closure $\operatorname{MM}(X)$, and let the totally positive kernel density estimator be the estimator constructed from this closure…

Let $f$ be an MTP$_2$ density on $\mathbb R^d$, and let $\varphi_h$ be a scaled standard Gaussian density. Gaussian convolution conjecture. The convolution $f*\varphi_h$ remains MT…

A density $f$ on $d53d^d$ is totally positive if it satisfies the relevant total-positivity property, and let $\varphi$ denote the standard Gaussian density. Gaussian convolution c…

The paper considers adaptive kernel density estimation under local approximate differential privacy, using Lepski's method to select a bandwidth for estimating a density at a fixed…