Related papers: Consistency Bands for divergences measures
When the data do not conform to the hypothesis of a known sampling-variance, the fitting of a constant to a set of measured values is a long debated problem. Given the data, fitting would require to find what measurand value is the most…
Skewness measures can be used to measure the level of asymmetry of a distribution. Given the prevalence of statistical methods that assume underlying symmetry, and also the desire for symmetry in order to make meaningful judgements for…
We consider uniform moment convergence of lag-window spectral density estimates for univariate and multivariate stationary processes. Optimal rates of convergence are obtained under mild and easily verifiable conditions. Our theory…
Diffusion models have revolutionized various application domains, including computer vision and audio generation. Despite the state-of-the-art performance, diffusion models are known for their slow sample generation due to the extensive…
We deal with the stability issue for the determination of outgoing time-harmonic acoustic waves from their far-field patterns. We are especially interested in keeping as explicit as possible the dependence of our stability estimates on the…
This paper concerns the inverse source problems for the time-harmonic elastic and electromagnetic wave equations. The goal is to determine the external force and the electric current density from boundary measurements of the radiated wave…
This paper studies density estimation and regression analysis with contaminated data observed on the unit hypersphere S^d. Our methodology and theory are based on harmonic analysis on general S^d. We establish novel nonparametric density…
This work describes a novel image analysis approach to characterize the uniformity of objects in agglomerates by using the propagation of normal wavefronts. The problem of width uniformity is discussed and its importance for the…
We investigate the discrepancy principle for choosing smoothing parameters for kernel density estimation. The method is based on the distance between the empirical and estimated distribution functions. We prove some new positive and…
A large class of problems in sciences and engineering can be formulated as the general problem of constructing random intervals with pre-specified coverage probabilities for the mean. Wee propose a general approach for statistical inference…
We propose a new wavelet-based method for density estimation when the data are size-biased. More specifically, we consider a power of the density of interest, where this power exceeds 1/2. Warped wavelet bases are employed, where warping is…
Uniform convergence rates are provided for asymptotic representations of sample extremes. These bounds which are universal in the sense that they do not depend on the extreme value index are meant to be extended to arbitrary samples…
The uncertainty or the variability of the data may be treated by considering, rather than a single value for each data, the interval of values in which it may fall. This paper studies the derivation of basic description statistics for…
This paper is devoted to study the asymptotic stability of wave equations with constant coefficients coupled by velocities. By using Riesz basis approach, multiplier method and frequency domain approach respectively, we find the sufficient…
We extend balloon and sample-smoothing estimators, two types of variable-bandwidth kernel density estimators, by a shift parameter and derive their asymptotic properties. Our approach facilitates the unified study of a wide range of density…
For any kind of wave phenomenon one can find ways to derive the respective dispersion relation from experimental observations and measurements. This dispersion relation determines the structure of the wave equation and thus characterizes…
Contrast set consistency is a robustness measurement that evaluates the rate at which a model correctly responds to all instances in a bundle of minimally different examples relying on the same knowledge. To draw additional insights, we…
We estimate on a compact interval densities with isolated irregularities, such as discontinuities or discontinuities in some derivatives. From independent and identically distributed observations we construct a kernel estimator with…
The problem of testing hypothesis that a density function has no more than $\mu$ derivatives versus it has more than $\mu$ derivatives is considered. For a solution, the $L^2$ norms of wavelet orthogonal projections on some orthogonal…
We present a local density estimator based on first order statistics. To estimate the density at a point, $x$, the original sample is divided into subsets and the average minimum sample distance to $x$ over all such subsets is used to…