Related papers: Tight conditions for consistent variable selection…
Quantile regression has been successfully used to study heterogeneous and heavy-tailed data. Varying-coefficient models are frequently used to capture changes in the effect of input variables on the response as a function of an index or…
Bayesian nonparametric regression under a rescaled Gaussian process prior offers smoothness-adaptive function estimation with near minimax-optimal error rates. Hierarchical extensions of this approach, equipped with stochastic variable…
The purpose of this paper is to propose methodologies for statistical inference of low-dimensional parameters with high-dimensional data. We focus on constructing confidence intervals for individual coefficients and linear combinations of…
In typical high dimensional statistical inference problems, confidence intervals and hypothesis tests are performed for a low dimensional subset of model parameters under the assumption that the parameters of interest are unconstrained.…
We consider a multivariate time series model which represents a high dimensional vector process as a sum of three terms: a linear regression of some observed regressors, a linear combination of some latent and serially correlated factors,…
It is of importance to develop statistical techniques to analyze high-dimensional data in the presence of both complex dependence and possible outliers in real-world applications such as imaging data analyses. We propose a new robust…
Mixtures of regression are a powerful class of models for regression learning with respect to a highly uncertain and heterogeneous response variable of interest. In addition to being a rich predictive model for the response given some…
This paper introduces a novel nonparametric method for estimating high-dimensional dynamic covariance matrices with multiple conditioning covariates, leveraging random forests and supported by robust theoretical guarantees. Unlike…
Bayesian variable selection has gained much empirical success recently in a variety of applications when the number $K$ of explanatory variables $(x_1,...,x_K)$ is possibly much larger than the sample size $n$. For generalized linear…
This paper considers multiple regression procedures for analyzing the relationship between a response variable and a vector of covariates in a nonparametric setting where both tuning parameters and the number of covariates need to be…
Many conventional statistical procedures are extremely sensitive to seemingly minor deviations from modeling assumptions. This problem is exacerbated in modern high-dimensional settings, where the problem dimension can grow with and…
We propose a way of transforming the problem of conditional density estimation into a single nonparametric regression task via the introduction of auxiliary samples. This allows leveraging regression methods that work well in high…
Although a majority of the theoretical literature in high-dimensional statistics has focused on settings which involve fully-observed data, settings with missing values and corruptions are common in practice. We consider the problems of…
In genetic studies, not only can the number of predictors obtained from microarray measurements be extremely large, there can also be multiple response variables. Motivated by such a situation, we consider semiparametric dimension reduction…
Logistic regression involving high-dimensional covariates is a practically important problem. Often the goal is variable selection, i.e., determining which few of the many covariates are associated with the binary response. Unfortunately,…
We investigate the high-dimensional linear regression problem in the presence of noise correlated with Gaussian covariates. This correlation, known as endogeneity in regression models, often arises from unobserved variables and other…
This paper develops new tools to quantify uncertainty in optimal decision making and to gain insight into which variables one should collect information about given the potential cost of measuring a large number of variables. We investigate…
For a high-dimensional parameter of interest, tests based on quadratic statistics are known to have low power against subsets of the parameter space (henceforth, parameter subspaces). In addition, they typically involve an inverse…
We study the problem of variable selection in convex nonparametric regression. Under the assumption that the true regression function is convex and sparse, we develop a screening procedure to select a subset of variables that contains the…
High-dimensional linear models with endogenous variables play an increasingly important role in recent econometric literature. In this work we allow for models with many endogenous variables and many instrument variables to achieve…