相关论文: On sliced Cram\'er metrics

As estimators of location parameters, univariate trimmed means are well known for their robustness and efficiency. They can serve as robust alternatives to the sample mean while possessing high efficiencies at normal as well as heavy-tailed…

One of the prevailing ideas in geometric and topological data analysis is to provide descriptors that encode useful information about hidden objects from observed data. The Reeb graph is one such descriptor for a given scalar function. The…

The Fr\'echet distance is a popular distance measure for curves which naturally lends itself to fundamental computational tasks, such as clustering, nearest-neighbor searching, and spherical range searching in the corresponding metric…

We continue our study, initiated in our earlier paper, of Riemann surfaces with constant curvature and isolated conic singularities. Using the machinery developed in that earlier paper of extended configuration families of simple divisors,…

The present paper is devoted to a theoretical analysis of sliding friction under the influence of oscillations perpendicular to the sliding plane. In contrast to previous works we analyze the influence of the stiffness of the tribological…

As global ocean general circulation models are run at eddy-permitting resolutions, reproducing accurate growth rates of baroclinic instabilities is a major concern when choosing a discretization of the equations of motion. From this…

In this paper, we propose a new approach to the investigation of asymptotic properties of trimmed $L$-statistics and we apply it to the Cram\'{e}r type large deviation problem. Our results can be compared with ones in Callaert et al.(1982)…

Sliced Wasserstein distances preserve properties of classic Wasserstein distances while being more scalable for computation and estimation in high dimensions. The goal of this work is to quantify this scalability from three key aspects: (i)…

Associated to every closed, embedded submanifold $N$ in a connected Riemannian manifold $M$, there is the distance function $d_N$ which measures the distance of a point in $M$ from $N$. We analyze the square of this function and show that…

Cram\'er's moderate deviations give a quantitative estimate for the relative error of the normal approximation and provide theoretical justifications for many estimator used in statistics. In this paper, we establish self-normalized…

Plastic deformation of micron-scale crystalline solids exhibits stress-strain curves with significant sample-to-sample variations. It is a pertinent question if this variability is purely random or to some extent predictable. Here we show,…

We study the deformation of drops squeezed between the floor and ceiling of a microchannel and subjected to a hyperbolic flow. We observe that the maximum deformation of drops depends on both the drop size and the rate of strain of the…

To measure the quality of a set of vector quantization points a means of measuring the distance between a random point and its quantization is required. Common metrics such as the {\em Hamming} and {\em Euclidean} metrics, while…

We introduce a new method for studying length spectrum rigidity problems based on a combination of ideas from dynamical systems and geometric group theory. This allows us to compare the marked length spectrum of metrics and distance-like…

The purpose of the present paper is to establish explicit bounds on moderate deviation probabilities for a rather general class of geometric functionals enjoying the stabilization property, under Poisson input and the assumption of a…

We study metric perturbations and deformation theory for degenerate Z/2-harmonic 1-forms. For a natural class of degenerate examples, we prove that after a suitable perturbation of the ambient Riemannian metric, the form can be deformed to…

1. Parameter inference from distorted measurements is discussed. 2. Smeared measurements are unfolded without explicit regularization. The corresponding results are unbiased and permit to fit parameters and to apply quantitative…

Reeb graphs provide a method for studying the shape of a manifold by encoding the evolution and arrangement of level sets of a simple Morse function defined on the manifold. Since their introduction in computer graphics they have been…

We construct bounded, commuting projections for the three-dimensional de Rham complex with the additional property that the projections preserve the trace of functions/fields if the latter is a piecewise polynomial in the appropriate trace…

It is well-known that trimmed sample means are robust against heavy tails and data contamination. This paper analyzes the performance of trimmed means and related methods in two novel contexts. The first one consists of estimating…