Related papers: Polyspectral Mean Estimation of General Nonlinear …
We study here a sequence of secondary measures, so called because the set of secondary polynomials on a given term become orthogonal for the next measure. The main result is a formula making explicit the density of any term of the sequence,…
Motivated by population studies of Diffusion Tensor Imaging, the paper investigates the use of mean-based and dispersion-based permutation tests to define and compute the significance of a statistical test for data taking values on…
The bispectral problem is motivated by an effort to understand and extend a remarkable phenomenon in Fourier analysis on the real line: the operator of time-and-band limiting is an integral operator admitting a second-order differential…
We advocate a compressed sensing strategy that consists of multiplying the signal of interest by a wide bandwidth modulation before projection onto randomly selected vectors of an orthonormal basis. Firstly, in a digital setting with random…
We apply Bayesian statistics to the estimation of correlation functions. We give the probability distributions of auto- and cross-correlations as functions of the data. Our procedure uses the measured data optimally and informs about the…
An algorithm is presented which generates pairs of oscillatory random time series which have identical periodograms but differ in the number of oscillations. This result indicate the intrinsic limitations of spectral methods when it comes…
Partial mean with generated regressors arises in several econometric problems, such as the distribution of potential outcomes with continuous treatments and the quantile structural function in a nonseparable triangular model. This paper…
We consider the problem of estimating a signal from noisy circularly-translated versions of itself, called multireference alignment (MRA). One natural approach to MRA could be to estimate the shifts of the observations first, and infer the…
Existing permanental processes often impose constraints on kernel types or stationarity, limiting the model's expressiveness. To overcome these limitations, we propose a novel approach utilizing the sparse spectral representation of…
A key question in modern statistics is how to make fast and reliable inferences for complex, high-dimensional data. While there has been much interest in sparse techniques, current methods do not generalize well to data with nonlinear…
We consider the analysis of continuous repeated measurement outcomes that are collected through time, also known as longitudinal data. A standard framework for analysing data of this kind is a linear Gaussian mixed-effects model within…
A variety of estimators for the parameters of the Generalized Pareto distribution, the approximating distribution for excesses over a high threshold, have been proposed, always assuming the underlying data to be independent. We recently…
Cross-spectral analysis is a mathematical tool for extracting the power spectral density of a correlated signal from two time series in the presence of uncorrelated interfering signals. We demonstrate and explain a set of conditions where…
Discrimination between non-stationarity and long-range dependency is a difficult and long-standing issue in modelling financial time series. This paper uses an adaptive spectral technique which jointly models the non-stationarity and…
In a two-stage cluster sampling procedure, $n$ random populations are drawn independently from independent populations and a sub-sample of observations is taken in each of them. The estimator of the general mean of the observed variables is…
Point spread function (PSF) engineering is vital for precisely controlling the focus of light in computational imaging, with applications in neural imaging, fluorescence microscopy, and biophotonics. The PSF is derived from the magnitude of…
A class of multivariate spectral representations for real-valued nonstationary random variables is introduced, which is characterised by a general complex Gaussian distribution. In this way, the temporal signal properties -- harmonicity,…
For functional data lying on an unknown nonlinear low-dimensional space, we study manifold learning and introduce the notions of manifold mean, manifold modes of functional variation and of functional manifold components. These constitute…
Multivariate global polynomial approximations - such as polynomial chaos or stochastic collocation methods - are now in widespread use for sensitivity analysis and uncertainty quantification. The pseudospectral variety of these methods uses…
In this paper, we give a new covariation spectral representation of some non stationary symmetric $\alpha$-stable processes (S$\alpha$S). This representation is based on a weaker covariation pseudo additivity condition which is more general…