Related papers: Tests for covariance matrix with fixed or divergen…
We consider the problem of joint estimation of structured inverse covariance matrices. We perform the estimation using groups of measurements with different covariances of the same unknown structure. Assuming the inverse covariances to span…
This work proposes a novel procedure to test for common structures across two high-dimensional factor models. The introduced test allows to uncover whether two factor models are driven by the same loading matrix up to some linear…
This paper is motivated by the comparison of genetic networks based on microarray samples. The aim is to test whether the differences observed between two inferred Gaussian graphical models come from real differences or arise from…
A number of biomedical problems require performing many hypothesis tests, with an attendant need to apply stringent thresholds. Often the data take the form of a series of predictor vectors, each of which must be compared with a single…
Model checking plays an important role in linear regression as model misspecification seriously affects the validity and efficiency of regression analysis. In practice, model checking is often performed by subjectively evaluating the plot…
The assumption of separability is a simplifying and very popular assumption in the analysis of spatio-temporal or hypersurface data structures. It is often made in situations where the covariance structure cannot be easily estimated, for…
We consider estimation of the covariance matrix of a multivariate random vector under the constraint that certain covariances are zero. We first present an algorithm, which we call Iterative Conditional Fitting, for computing the maximum…
We propose a method for testing whether hierarchically ordered groups of potentially correlated variables are significant for explaining a response in a high-dimensional linear model. In presence of highly correlated variables, as is very…
Missing data occur frequently in a wide range of applications. In this paper, we consider estimation of high-dimensional covariance matrices in the presence of missing observations under a general missing completely at random model in the…
Hierarchical inference in (generalized) regression problems is powerful for finding significant groups or even single covariates, especially in high-dimensional settings where identifiability of the entire regression parameter vector may be…
In this paper, we investigate the testing problem that the spectral density matrices of several, not necessarily independent, stationary processes are equal. Based on an $L_2$-type test statistic, we propose a new nonparametric approach,…
We present new families of goodness-of-fit tests of uniformity on a full-dimensional set $W\subset\R^d$ based on statistics related to edge lengths of random geometric graphs. Asymptotic normality of these statistics is proven under the…
The asymptotic normality for a large family of eigenvalue statistics of a general sample covariance matrix is derived under the ultra-high dimensional setting, that is, when the dimension to sample size ratio $p/n \to \infty$. Based on this…
So-called linear rank statistics provide a means for distribution-free (even in finite samples), yet highly flexible, two-sample testing in the setting of univariate random variables. Their flexibility derives from a choice of weights that…
In this self-contained chapter, we revisit a fundamental problem of multivariate statistics: estimating covariance matrices from finitely many independent samples. Based on massive Multiple-Input Multiple-Output (MIMO) systems we illustrate…
A dimension reduction-based adaptive-to-model test is proposed for significance of a subset of covariates in the context of a nonparametric regression model. Unlike existing local smoothing significance tests, the new test behaves like a…
Graph (or network) is a mathematical structure that has been widely used to model relational data. As real-world systems get more complex, multilayer (or multiple) networks are employed to represent diverse patterns of relationships among…
Biclustering is a method for detecting homogeneous submatrices in a given observed matrix, and it is an effective tool for relational data analysis. Although there are many studies that estimate the underlying bicluster structure of a…
There is an increasing interest in algorithms to learn invariant correlations across training environments. A big share of the current proposals find theoretical support in the causality literature but, how useful are they in practice? The…
We consider testing the significance of a subset of covariates in a nonparametric regression. These covariates can be continuous and/or discrete. We propose a new kernel-based test that smoothes only over the covariates appearing under the…