Related papers: A new recentered confidence sphere for the multiva…

We derive a probability distribution, confidence intervals and statistics of the quality (Q) factor of an arbitrarily shaped mode-stirred reverberation chamber, based on ensemble distributions of the idealized random cavity field with…

The contact values $g_{ij}(\sigma_{ij})$ of the radial distribution functions of a $d$-dimensional mixture of (additive) hard spheres are considered. A `universality' assumption is put forward, according to which…

Confidence sets from i.i.d. data are constructed for the extrinsic mean of a probabilty measure P on spheres, real projective spaces, and complex projective spaces, as well as Grassmann manifolds, with the latter three embedded by the…

We consider quasi-admissibility/inadmissibility of Stein-type shrinkage estimators of the mean of a multivariate normal distribution with covariance matrix an unknown multiple of the identity. Quasi-admissibility/inadmissibility is defined…

Let $\Theta^{(n)}$ be a random vector uniformly distributed on the unit sphere $\mathbb S^{n-1}$ in $\mathbb R^n$. Consider the projection of the uniform distribution on the cube $[-1,1]^n$ to the line spanned by $\Theta^{(n)}$. The…

We consider density estimators based on the nearest neighbors method applied to discrete point distibutions in spaces of arbitrary dimensionality. If the density is constant, the volume of a hypersphere centered at a random location is…

We prove a general theorem providing smoothed analysis estimates for conic condition numbers of problems of numerical analysis. Our probability estimates depend only on geometric invariants of the corresponding sets of ill-posed inputs.…

A recent proposal in which the equation of state of a polydisperse hard-sphere mixture is mapped onto that of the one-component fluid is extrapolated beyond the freezing point to estimate the jamming packing fraction $\phi_\text{J}$ of the…

We investigate the asymptotic normality of the posterior distribution in the discrete setting, when model dimension increases with sample size. We consider a probability mass function $\theta_0$ on $\mathbbm{N}\setminus \{0\}$ and a…

Let $X_1,\ldots,X_n$ be a random sample from the Gamma distribution with density $f(x)=\lambda^{\alpha}x^{\alpha-1}e^{-\lambda x}/\Gamma(\alpha)$, $x>0$, where both $\alpha>0$ (the shape parameter) and $\lambda>0$ (the reciprocal scale…

The seminal result of Johnson and Lindenstrauss on random embeddings has been intensively studied in applied and theoretical computer science. Despite that vast body of literature, we still lack of complete understanding of statistical…

In the regression model with errors in variables, we observe $n$ i.i.d. copies of $(Y,Z)$ satisfying $Y=f_{\theta^0}(X)+\xi$ and $Z=X+\epsilon$ involving independent and unobserved random variables $X,\xi,\epsilon$ plus a regression…

Let $X,U,Y$ be spherically symmetric distributed having density $$\eta^{d +k/2} \, f\left(\eta(\|x-\theta|^2+ \|u\|^2 + \|y-c\theta\|^2 ) \right)\,,$$ with unknown parameters $\theta \in \mathbb{R}^d$ and $\eta>0$, and with known density…

Rotationally symmetric distributions on the p-dimensional unit hypersphere, extremely popular in directional statistics, involve a location parameter theta that indicates the direction of the symmetry axis. The most classical way of…

For estimating a lower bounded location or mean parameter for a symmetric and logconcave density, we investigate the frequentist performance of the $100(1-\alpha)%$ Bayesian HPD credible set associated with priors which are truncations of…

We show that the family of probability measures on the $n$-dimensional unit sphere, having density proportional to: \[ S^n \ni y \mapsto \frac{1}{|y - x|^{n+\alpha}}, \] satisfies the Curvature-Dimension condition…

We consider the problem of numerically evaluating the expected value of a smooth bounded function of a chi-distributed random variable, divided by the square root of the number of degrees of freedom. This problem arises in the contexts of…

The Sliced-Wasserstein (SW) distance between probability measures is defined as the average of the Wasserstein distances resulting for the associated one-dimensional projections. As a consequence, the SW distance can be written as an…

Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…

This paper aims at presenting a simulative analysis of the main properties of a new $R$-estimator of shape matrices in Complex Elliptically Symmetric (CES) distributed observations. First proposed by Hallin, Oja and Paindaveine for the…