Related papers: Non-Euclidean statistics for covariance matrices, …
We study statistical inference on unit roots and cointegration for time series in a Hilbert space. We develop statistical inference on the number of common stochastic trends embedded in the time series, i.e., the dimension of the…
Several measures of non-convexity (departures from convexity) have been introduced in the literature, both for sets and functions. Some of them are of geometric nature, while others are more of topological nature. We address the statistical…
We propose a new statistical observation scheme of diffusion processes named convolutional observation, where it is possible to deal with smoother observation than ordinary diffusion processes by considering convolution of diffusion…
In this paper, a shrinkage estimator for the population mean is proposed under known quadratic loss functions with unknown covariance matrices. The new estimator is non-parametric in the sense that it does not assume a specific parametric…
In brain imaging, the image acquisition and processing processes themselves are likely to introduce noise to the images. It is therefore imperative to reduce the noise while preserving the geometric details of the anatomical structures for…
Tensor regression methods have been widely used to predict a scalar response from covariates in the form of a multiway array. In many applications, the regions of tensor covariates used for prediction are often spatially connected with…
Preclinical diffusion MRI (dMRI) has proven value in methods development and validation, characterizing the biological basis of diffusion phenomena, and comparative anatomy. While dMRI enables in vivo non-invasive characterization of…
Based on the properties of distributions and measures with discrete support, we investigate temperate almost periodic distributions on the Euclidean space and connection with their Fourier transforms. We also study relations between the…
Standard diffusion models are flexible estimators of complex distributions, but they do not encode causal structures and therefore do not by themselves support causal analysis. We propose a causality-encoded diffusion framework that…
We investigate the non-Gaussian features in the distribution of the matter power spectrum multipoles. Using the COVMOS method, we generate 100\,000 mock realisations of dark matter density fields in both real and redshift space across…
Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to…
The covariance matrix of the matter power spectrum is a key element of the statistical analysis of galaxy clustering data. Independent realisations of observational measurements can be used to sample the covariance, nevertheless statistical…
Multivariate statistical methods are widely used throughout the sciences, including microscopy, however, their utilisation for analysis of electron backscatter diffraction (EBSD) data has not been adequately explored. The basic aim of most…
Application of fractional calculus to the description of anomalous diffusion and relaxation processes in complex media provided one of the most impressive impulses to the development of statistical physics during the last decade. In…
We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may…
This chapter discusses the importance of incorporating three-dimensional symmetries in the context of statistical learning models geared towards the interpolation of the tensorial properties of atomic-scale structures. We focus on Gaussian…
Statistical inference on large-dimensional tensor data has been extensively studied in the literature and widely used in economics, biology, machine learning, and other fields, but how to generate a structured tensor with a target…
This paper proposes new estimators for the propensity score that aim to maximize the covariate distribution balance among different treatment groups. Heuristically, our proposed procedure attempts to estimate a propensity score model by…
We prove concentration inequalities for several models of non-linear random matrices. As corollaries we obtain estimates for linear spectral statistics of the conjugate kernel of neural networks and non-commutative polynomials in (possibly…
In this paper, we study a kernel smoothing approach for denoising a tensor field. Particularly, both simulation studies and theoretical analysis are conducted to understand the effects of the noise structure and the structure of the tensor…