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Testing heteroscedasticity of the errors is a major challenge in high-dimensional regressions where the number of covariates is large compared to the sample size. Traditional procedures such as the White and the Breusch-Pagan tests…

We consider covariate adjusted regression (CAR), a regression method for situations where predictors and response are observed after being distorted by a multiplicative factor. The distorting factors are unknown functions of an observable…

This paper offers a new method for estimation and forecasting of the volatility of financial time series when the stationarity assumption is violated. Our general local parametric approach particularly applies to general varying-coefficient…

While inference-time scaling has significantly enhanced generative quality in large language and diffusion models, its application to vector-quantized (VQ) visual autoregressive modeling (VAR) remains unexplored. We introduce VAR-Scaling,…

We propose a non-asymptotic convergence analysis of a two-step approach to learn a conditional value-at-risk (VaR) and a conditional expected shortfall (ES) using Rademacher bounds, in a non-parametric setup allowing for heavy-tails on the…

A standard model of (conditional) heteroscedasticity, i.e., the phenomenon that the variance of a process changes over time, is the Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) model, which is especially important for…

We study the problem of modelling high-dimensional, heavy-tailed time series data via a factor-adjusted vector autoregressive (VAR) model, which simultaneously accounts for pervasive co-movements of the variables by a handful of factors, as…

Autonomous Vehicles (AVs) are often tested in simulation to estimate the probability they will violate safety specifications. Two common issues arise when using existing techniques to produce this estimation: If violations occur rarely,…

If uncorrelated random variables have a common expected value and decreasing variances then the variance of a sample mean is decreasing with the number of observations. Unfortunately, this natural and desirable Variance Reduction Property…

Through sequential construction of posteriors on observing data online, Bayes' theorem provides a natural framework for continual learning. We develop Variational Auto-Regressive Gaussian Processes (VAR-GPs), a principled posterior updating…

This study delves into the domain of dynamical systems, specifically the forecasting of dynamical time series defined through an evolution function. Traditional approaches in this area predict the future behavior of dynamical systems by…

We derive new theoretical results on the properties of the adaptive least absolute shrinkage and selection operator (adaptive lasso) for time series regression models. In particular, we investigate the question of how to conduct finite…

The Lasso method is known to exhibit instability in the presence of highly correlated features, often leading to an arbitrary selection of predictors. This issue manifests itself in two primary error types: the erroneous omission of…

Causality graphs are routinely estimated in social sciences, natural sciences, and engineering due to their capacity to efficiently represent the spatiotemporal structure of multivariate data sets in a format amenable for human…

In the heteroscedastic linear model, the weighted least squares (WLS) estimate of the model coefficients is more efficient than the ordinary least squares (OLS) esti- mate. However, the practical application of WLS is challenging because it…

The paper presents a systematic theory for asymptotic inference of autocovariances of stationary processes. We consider nonparametric tests for serial correlations based on the maximum (or ${\cal L}^\infty$) and the quadratic (or ${\cal…

We consider the problem of estimating the parameters of a linear univariate autoregressive model with sub-Gaussian innovations from a limited sequence of consecutive observations. Assuming that the parameters are compressible, we analyze…

The iteratively reweighted least squares method (IRLS) is a popular technique used in practice for solving regression problems. Various versions of this method have been proposed, but their theoretical analyses failed to capture the good…

Missing covariate data pose a significant challenge to statistical inference and machine learning, particularly for classification tasks like logistic regression. Classical iterative approaches (EM, multiple imputation) are often…

Panel vector auto-regressive (VAR) models are widely used to capture the dynamics of multivariate time series across different subpopulations, where each subpopulation shares a common set of variables. In this work, we propose a panel VAR…