Related papers: Adaptive Test Procedure for High Dimensional Regre…
We propose new statistical tests, in high-dimensional settings, for testing the independence of two random vectors and their conditional independence given a third random vector. The key idea is simple, i.e., we first transform each…
In this paper, we introduce the first principled adaptive-sampling procedure for learning a convex function in the $L_\infty$ norm, a problem that arises often in the behavioral and social sciences. We present a function-specific measure of…
We review recent results for high-dimensional sparse linear regression in the practical case of unknown variance. Different sparsity settings are covered, including coordinate-sparsity, group-sparsity and variation-sparsity. The emphasis is…
We propose dimension reduction methods for sparse, high-dimensional multivariate response regression models. Both the number of responses and that of the predictors may exceed the sample size. Sometimes viewed as complementary, predictor…
We leverage recent advances in heavy-tail approximations for global hypothesis testing with dependent studies to construct approximate confidence regions without modeling or estimating their dependence structures. A non-rejection region is…
This paper is concerned with high-dimensional panel data models where the number of regressors can be much larger than the sample size. Under the assumption that the true parameter vector is sparse we propose a panel-Lasso estimator and…
We develop a convex framework for spatially varying coefficient quantile regression that, for each predictor, separates a location-invariant \emph{global} effect from a \emph{spatial deviation}. An adaptive group penalty selects whether a…
We propose a general method for constructing confidence intervals and statistical tests for single or low-dimensional components of a large parameter vector in a high-dimensional model. It can be easily adjusted for multiplicity taking…
We consider the adaptive Lasso estimator with componentwise tuning in the framework of a low-dimensional linear regression model. In our setting, at least one of the components is penalized at the rate of consistent model selection and…
To estimate a sparse linear model from data with Gaussian noise, consilience from lasso and compressed sensing literatures is that thresholding estimators like lasso and the Dantzig selector have the ability in some situations to identify…
As a common step in refining their scientific inquiry, investigators are often interested in performing some screening of a collection of given statistical hypotheses. For example, they may wish to determine whether any one of several…
Combining individual p-values to aggregate multiple small effects has a long-standing interest in statistics, dating back to the classic Fisher's combination test. In modern large-scale data analysis, correlation and sparsity are common…
Recent work has focused on the problem of conducting linear regression when the number of covariates is very large, potentially greater than the sample size. To facilitate this, one useful tool is to assume that the model can be well…
This paper studies inference for the mean vector of a high-dimensional $U$-statistic. In the era of Big Data, the dimension $d$ of the $U$-statistic and the sample size $n$ of the observations tend to be both large, and the computation of…
The problem of detecting changes in covariance for a single pair of features has been studied in some detail, but may be limited in importance or general applicability. In contrast, testing equality of covariance matrices of a {\it set} of…
We consider the classification problem of a high-dimensional mixture of two Gaussians with general covariance matrices. Using the replica method from statistical physics, we investigate the asymptotic behavior of a general class of…
In this thesis we study adaptive nonparametric regression with noise misspecification and the complexity of approximation of random fields in dependence of the dimension. First, we consider the problem of pointwise estimation in…
The package High-dimensional Metrics (\Rpackage{hdm}) is an evolving collection of statistical methods for estimation and quantification of uncertainty in high-dimensional approximately sparse models. It focuses on providing confidence…
Many data mining and statistical machine learning algorithms have been developed to select a subset of covariates to associate with a response variable. Spurious discoveries can easily arise in high-dimensional data analysis due to enormous…
Asymptotic methods for hypothesis testing in high-dimensional data usually require the dimension of the observations to increase to infinity, often with an additional condition on its rate of increase compared to the sample size. On the…