Related papers: High-dimensional Varying Index Coefficient Models …

In multivariate regression, when covariates are numerous, it is often reasonable to assume that only a small number of them has predictive information. In some medical applications for instance, it is believed that only a few genes out of…

We study the problem of parameter estimation for time-series possessing two, widely separated, characteristic time scales. The aim is to understand situations where it is desirable to fit a homogenized singlescale model to such multiscale…

We consider hypotheses testing problems for three parameters in high-dimensional linear models with minimal sparsity assumptions of their type but without any compatibility conditions. Under this framework, we construct the first…

In this paper, we present a novel framework incorporating a combination of sparse models in different domains. We posit the observed data as generated from a linear combination of a sparse Gaussian Markov model (with a sparse precision…

Statistical models often include thousands of parameters. However, large models decrease the investigator's ability to interpret and communicate the estimated parameters. Reducing the dimensionality of the parameter space in the estimation…

The covariance matrix plays a fundamental role in many modern exploratory and inferential statistical procedures, including dimensionality reduction, hypothesis testing, and regression. In low-dimensional regimes, where the number of…

High-dimensional predictive models, those with more measurements than observations, require regularization to be well defined, perform well empirically, and possess theoretical guarantees. The amount of regularization, often determined by…

Many applications involve estimation of a signal matrix from a noisy data matrix. In such cases, it has been observed that estimators that shrink or truncate the singular values of the data matrix perform well when the signal matrix has…

Cointegration analysis is used to estimate the long-run equilibrium relations between several time series. The coefficients of these long-run equilibrium relations are the cointegrating vectors. In this paper, we provide a sparse estimator…

The classical vector autoregressive model is a fundamental tool for multivariate time series analysis. However, it involves too many parameters when the number of time series and lag order are even moderately large. This paper proposes to…

This article studies bootstrap inference for high dimensional weakly dependent time series in a general framework of approximately linear statistics. The following high dimensional applications are covered: (1) uniform confidence band for…

Graphical models are commonly used to represent conditional dependence relationships between variables. There are multiple methods available for exploring them from high-dimensional data, but almost all of them rely on the assumption that…

The geometric median covariation matrix is a robust multivariate indicator of dispersion which can be extended without any difficulty to functional data. We define estimators, based on recursive algorithms, that can be simply updated at…

High-dimensional data with hundreds of thousands of observations are becoming commonplace in many disciplines. The analysis of such data poses many computational challenges, especially when the observations are correlated over time and/or…

Correlated random fields are a common way to model dependence struc- tures in high-dimensional data, especially for data collected in imaging. One important parameter characterizing the degree of dependence is the asymp- totic variance…

Time-varying parameter VARs with stochastic volatility are routinely used for structural analysis and forecasting in settings involving a few endogenous variables. Applying these models to high-dimensional datasets has proved to be…

High-dimensional inference refers to problems of statistical estimation in which the ambient dimension of the data may be comparable to or possibly even larger than the sample size. We study an instance of high-dimensional inference in…

To model modern large-scale datasets, we need efficient algorithms to infer a set of $P$ unknown model parameters from $N$ noisy measurements. What are fundamental limits on the accuracy of parameter inference, given finite signal-to-noise…

The analysis of non-real-valued data, such as binary time series, has attracted great interest in recent years. This manuscript proposes a post-selection estimator for estimating the coefficient matrices of a high-dimensional generalized…

We study the problem of estimating the leading eigenvectors of a high-dimensional population covariance matrix based on independent Gaussian observations. We establish lower bounds on the rates of convergence of the estimators of the…