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Leading methods for support recovery in high-dimensional regression, such as Lasso, have been well-studied and their limitations in the context of correlated design have been characterized with precise incoherence conditions. In this work,…
In dealing with high-dimensional data, factor models are often used for reducing dimensions and extracting relevant information. The spectrum of covariance matrices from power data exhibits two aspects: 1) bulk, which arises from random…
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…
This paper studies the case of possibly high-dimensional covariates in the regression discontinuity design (RDD) analysis. In particular, we propose estimation and inference methods for the RDD models with covariate selection which perform…
In this paper, a Mixed Data Sampling (MIDAS) model is studied when both low and high frequency variables are contaminated with measurement error. It is shown that the profile likelihood estimator becomes inconsistent in the presence of…
In our paper, we focus on robust variable selection for missing data and measurement error. Missing data and measurement errors can lead to confusing data distribution. We propose an exponential loss function with a tuning parameter to…
In this paper, we propose a novel high-dimensional time-varying coefficient estimator for noisy high-frequency observations with a factor structure. In high-frequency finance, we often observe that noises dominate the signal of underlying…
Penalized logistic regression is extremely useful for binary classification with large number of covariates (higher than the sample size), having several real life applications, including genomic disease classification. However, the…
In this paper, we consider the problem of recovering a sparse signal from noisy linear measurements using the so called LASSO formulation. We assume a correlated Gaussian design matrix with additive Gaussian noise. We precisely analyze the…
Medical studies that depend on electronic health records (EHR) data are often subject to measurement error, as the data are not collected to support research questions under study. These data errors, if not accounted for in study analyses,…
Compositional data arise in many areas of research in the natural and biomedical sciences. One prominent example is in the study of the human gut microbiome, where one can measure the relative abundance of many distinct microorganisms in a…
Machine learning methods are used to discover complex nonlinear relationships in biological and medical data. However, sophisticated learning models are computationally unfeasible for data with millions of features. Here we introduce the…
When a series of (related) linear models has to be estimated it is often appropriate to combine the different data-sets to construct more efficient estimators. We use $\ell_1$-penalized estimators like the Lasso or the Adaptive Lasso which…
High-dimensional compositional data are prevalent in many applications. The simplex constraint poses intrinsic challenges to inferring the conditional dependence relationships among the components forming a composition, as encoded by a…
We consider the problem of identifying significant predictors in large data bases, where the response variable depends on the linear combination of explanatory variables through an unknown link function, corrupted with the noise from the…
In recent years, there has been considerable theoretical development regarding variable selection consistency of penalized regression techniques, such as the lasso. However, there has been relatively little work on quantifying the…
Large-scale empirical data, the sample size and the dimension are high, often exhibit various characteristics. For example, the noise term follows unknown distributions or the model is very sparse that the number of critical variables is…
Matrix-covariate is now frequently encountered in many biomedical researches. It is common to fit conventional statistical models by vectorizing matrix-covariate. This strategy, however, results in a large number of parameters, while the…
This paper tackles the problem of robust covariance matrix estimation when the data is incomplete. Classical statistical estimation methodologies are usually built upon the Gaussian assumption, whereas existing robust estimation ones assume…
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…