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Statistical identification of possibly non-fundamental SVARMA models requires structural errors: (i) to be an i.i.d process, (ii) to be mutually independent across components, and (iii) each of them must be non-Gaussian distributed. Hence,…
We study the spherical cap packing problem with a probabilistic approach. Such probabilistic considerations result in an asymptotic sharp universal uniform bound on the maximal inner product between any set of unit vectors and a…
Model selection in penalized regression critically depends on an accurate assessment of model complexity, commonly quantified through the effective degrees of freedom. While the Lasso admits a simple and unbiased characterization, given by…
Causal discovery with latent variables is a fundamental task. Yet most existing methods rely on strong structural assumptions, such as enforcing specific indicator patterns for latents or restricting how they can interact with others. We…
Undirected graphical models are widely used to model the conditional independence structure of vector-valued data. However, in many modern applications, for example those involving EEG and fMRI data, observations are more appropriately…
High-dimensional linear regression has been thoroughly studied in the context of independent and identically distributed data. We propose to investigate high-dimensional regression models for independent but non-identically distributed…
In this paper, we develop invariance-based procedures for testing and inference in high-dimensional regression models. These procedures, also known as randomization tests, provide several important advantages. First, for the global null…
In a linear regression model of fixed dimension $p \leq n$, we construct confidence regions for the unknown parameter vector based on the Lasso estimator that uniformly and exactly hold the prescribed in finite samples as well as in an…
We study theoretical properties of regularized robust M-estimators, applicable when data are drawn from a sparse high-dimensional linear model and contaminated by heavy-tailed distributions and/or outliers in the additive errors and…
Statistically equivalent blocks are not frequently considered in the context of nonparametric two-sample hypothesis testing. Despite the limited exposure, this paper shows that a number of classical nonparametric hypothesis tests can be…
In structured prediction, target objects have rich internal structure which does not factorize into independent components and violates common i.i.d. assumptions. This challenge becomes apparent through the exponentially large output space…
Biased sampling designs can be highly efficient when studying rare (binary) or low variability (continuous) endpoints. We consider longitudinal data settings in which the probability of being sampled depends on a repeatedly measured…
Additive regression models are actively researched in the statistical field because of their usefulness in the analysis of responses determined by non-linear relationships with multivariate predictors. In this kind of statistical models,…
This paper studies the construction of adaptive confidence intervals under Huber's contamination model when the contamination proportion is unknown. For the robust confidence interval of a Gaussian mean, we show that the optimal length of…
Complex survey data are usually collected following complex sampling designs. Accounting for the sampling design is essential to obtain unbiased estimates and valid inferences when analyzing complex survey data. The area under the receiver…
Quasi-experimental research designs, such as regression discontinuity and interrupted time series, allow for causal inference in the absence of a randomized controlled trial, at the cost of additional assumptions. In this paper, we provide…
New upper bounds are developed for the $L_2$ distance between $\xi/\text{Var}[\xi]^{1/2}$ and linear and quadratic functions of $z\sim N(0,I_n)$ for random variables of the form $\xi=bz^\top f(z) - \text{div} f(z)$. The linear approximation…
We consider the nonparametric regression problem with multiple predictors and an additive error, where the regression function is assumed to be coordinatewise nondecreasing. We propose a Bayesian approach to make an inference on the…
Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…
We suggest novel correlation coefficients which equal the maximum correlation for a class of bivariate Lancaster distributions while being only slightly smaller than maximum correlation for a variety of further bivariate distributions. In…