相关论文: Detecting sparse cone alternatives for Gaussian ra…

This paper provides novel results for the recovery of signals from undersampled measurements based on analysis $\ell_1$-minimization, when the analysis operator is given by a frame. We both provide so-called uniform and nonuniform recovery…

We propose an estimator for the mean of random variables in separable real Banach spaces using the empirical characteristic function. Assuming that the covariance operator of the random variable is bounded in a precise sense, we show that…

Many complex phenomena occurring in physics,chemistry, biology, finance, etc. can be reduced, by some projection process, to a 1-d stochastic Differential Equation (SDE) for the variable of interest. Typically, this SDE is both non-linear…

dentifying associations among biological variables is a major challenge in modern quantitative biological research, particularly given the systemic and statistical noise endemic to biological systems. Drug sensitivity data has proven to be…

In this paper, we consider a classic problem concerning the high excursion probabilities of a Gaussian random field $f$ living on a compact set $T$. We develop efficient computational methods for the tail probabilities $P(\sup_T f(t) > b)$…

We develop goodness-of-fit tests for max-stable random fields, which are used to model heavy-tailed spatial data. The test statistics are constructed based on the Fourier transforms of the indicators of extreme values in the heavy-tailed…

Sparse linear regression methods including the well-known LASSO and the Dantzig selector have become ubiquitous in the engineering practice, including in medical imaging. Among other tasks, they have been successfully applied for the…

Gaussian processes are the leading class of distributions on random functions, but they suffer from well known issues including difficulty scaling and inflexibility with respect to certain shape constraints (such as nonnegativity). Here we…

Diffusive search for a static target is a common problem in statistical physics with numerous applications in chemistry and biology. We look at this problem from a different perspective and investigate the statistics of encounters between…

In this paper we derive weak limits for the discretization errors of sampling barrier-hitting and extreme events of Brownian motion by using the Euler discretization simulation method. Specifically, we consider the Euler discretization…

We consider parametric estimation of the continuous part of a class of ergodic diffusions with jumps based on high-frequency samples. Various papers previously proposed threshold based methods, which enable us to distinguish whether…

We consider the problem of detecting a change in mean in a sequence of Gaussian vectors. Under the alternative hypothesis, the change occurs only in some subset of the components of the vector. We propose a test of the presence of a…

A fundamental problem of statistical data analysis, distribution density estimation by experimental data, is considered. A new method with optimal asymptotic behavior, the root density estimator, is developed. The method proposed may be…

Graphical and sparse (inverse) covariance models have found widespread use in modern sample-starved high dimensional applications. A part of their wide appeal stems from the significantly low sample sizes required for the existence of…

It has always been a big challenge to identify subtle changes in Electroencephalogram (EEG) signals. Minor differences often lead to vital decisions, for example, which grade a certain tumour belong to or whether a haemorrhage can result in…

Statistical data is often analyzed as a contingency table, sometimes with empty cells called zeros. Such sparse tables can be due to scarse observations classified in numerous categories, as for example in genetic association studies. Thus,…

Statistical data is often analyzed as a contingency table, sometimes with empty cells called zeros. Such sparse tables can be due to scarse observations classified in numerous categories, as for example in genetic association studies. Thus,…

We prove new explicit upper bounds on the leverage scores of Fourier sparse functions under both the Gaussian and Laplace measures. In particular, we study $s$-sparse functions of the form $f(x) = \sum_{j=1}^s a_j e^{i \lambda_j x}$ for…

Functional magnetic resonance imaging (fMRI) aims to locate activated regions in human brains when specific tasks are performed. The conventional tool for analyzing fMRI data applies some variant of the linear model, which is restrictive in…

We revisit the problem of mean estimation in the Gaussian sequence model with $\ell_p$ constraints for $p \in [0, \infty]$. We demonstrate two phenomena for the behavior of the maximum likelihood estimator (MLE), which depend on the noise…