Related papers: Adaptive test for large covariance matrices with m…
The Riemannian geometry of covariance matrices has been essential to several successful applications, in computer vision, biomedical signal and image processing, and radar data processing. For these applications, an important ongoing…
When data analysts train a classifier and check if its accuracy is significantly different from chance, they are implicitly performing a two-sample test. We investigate the statistical properties of this flexible approach in the…
Supervised learning is often affected by a covariate shift in which the marginal distributions of instances (covariates $x$) of training and testing samples $\mathrm{p}_\text{tr}(x)$ and $\mathrm{p}_\text{te}(x)$ are different but the label…
Estimating a sparse covariance matrix is a fundamental problem in high-dimensional statistics. However, thresholding methods developed for independent data are generally not directly applicable to high-dimensional time series, where…
For symmetric random matrices with correlated entries, which are functions of independent random variables, we show that the asymptotic behavior of the empirical eigenvalue distribution can be obtained by analyzing a Gaussian matrix with…
The problem of detecting correlations from samples of a high-dimensional Gaussian vector has recently received a lot of attention. In most existing work, detection procedures are provided with a full sample. However, following common wisdom…
Covariance matrices of random vectors contain information that is crucial for modelling. Specific structures and patterns of the covariances (or correlations) may be used to justify parametric models, e.g., autoregressive models. Until now,…
Given a set of incomplete observations, we study the nonparametric problem of testing whether data are Missing Completely At Random (MCAR). Our first contribution is to characterise precisely the set of alternatives that can be…
We study concentration in spectral norm of nonparametric estimates of correlation matrices. We work within the confine of a Gaussian copula model. Two nonparametric estimators of the correlation matrix, the sine transformations of the…
Discrepancy measures between probability distributions, often termed statistical distances, are ubiquitous in probability theory, statistics and machine learning. To combat the curse of dimensionality when estimating these distances from…
We provide efficient algorithms for the problem of distribution learning from high-dimensional Gaussian data where in each sample, some of the variable values are missing. We suppose that the variables are missing not at random (MNAR). The…
Robust statistical inference often faces a severe computational-statistical gap when dealing with complex parameter spaces. We investigate minimax signal detection in the Gaussian sequence model under strong $\epsilon$-contamination, where…
We study the problem of detecting a change in the mean of one-dimensional Gaussian process data. This problem is investigated in the setting of increasing domain (customarily employed in time series analysis) and in the setting of fixed…
We consider the equivalent problems of estimating the residual variance, the proportion of explained variance $\eta$ and the signal strength in a high-dimensional linear regression model with Gaussian random design. Our aim is to understand…
Residual marked empirical process-based tests are commonly used in regression models. However, they suffer from data sparseness in high-dimensional space when there are many covariates. This paper has three purposes. First, we suggest a…
We consider high-dimensional measurement errors with high-frequency data. Our objective is on recovering the high-dimensional cross-sectional covariance matrix of the random errors with optimality. In this problem, not all components of the…
Motivated mainly by applications to partial differential equations with random coefficients, we introduce a new class of Monte Carlo estimators, called Toeplitz Monte Carlo (TMC) estimator for approximating the integral of a multivariate…
We study the problem of high-dimensional covariance estimation under the constraint that the partial correlations are nonnegative. The sign constraints dramatically simplify estimation: the Gaussian maximum likelihood estimator is well…
The need to test whether two random vectors are independent has spawned a large number of competing measures of dependence. We are interested in nonparametric measures that are invariant under strictly increasing transformations, such as…
We consider a $d$-dimensional continuous martingale $X(t)$ with quadratic variation matrix $\langle X\rangle_t=\int_0^t \Sigma(s)\,ds$ and develop tests for the rank of its spot covariance matrix $\Sigma(t)$, $t\in[0,1]$. The process $X$ is…