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In this paper, we study the hard and soft support vector regression techniques applied to a set of $n$ linear measurements of the form $y_i=\boldsymbol{\beta}_\star^{T}{\bf x}_i +n_i$ where $\boldsymbol{\beta}_\star$ is an unknown vector,…
In many important statistical analyses, the number of covariates $p$ often exceeds the data size $n$, a regime commonly referred to as high-dimensional. While considerable progress has been made in high-dimensional regression under the…
The paper concerns inference in the ill-conditioned functional response model, which is a part of functional data analysis. In this regression model, the functional response is modeled using several independent scalar variables. To verify…
This paper studies the inference of the regression coefficient matrix under multivariate response linear regressions in the presence of hidden variables. A novel procedure for constructing confidence intervals of entries of the coefficient…
In this article, we investigate the asymptotic properties of Bayesian multiple testing procedures under general dependent setup, when the sample size and the number of hypotheses both tend to infinity. Specifically, we investigate strong…
This paper is concerned with estimation and inference for ultrahigh dimensional partially linear single-index models. The presence of high dimensional nuisance parameter and nuisance unknown function makes the estimation and inference…
This paper studies the asymptotics of resampling without replacement in the proportional regime where dimension $p$ and sample size $n$ are of the same order. For a given dataset $(X,y)\in \mathbb{R}^{n\times p}\times \mathbb{R}^n$ and…
These lecture notes provide an overview of existing methodologies and recent developments for estimation and inference with high dimensional time series regression models. First, we present main limit theory results for high dimensional…
We consider non-parametric estimation and inference of conditional moment models in high dimensions. We show that even when the dimension $D$ of the conditioning variable is larger than the sample size $n$, estimation and inference is…
For a high-dimensional linear model with a finite number of covariates measured with error, we study statistical inference on the parameters associated with the error-prone covariates, and propose a new corrected decorrelated score test and…
Regression adjustment is broadly applied in randomized trials under the premise that it usually improves the precision of a treatment effect estimator. However, previous work has shown that this is not always true. To further understand…
In this paper, we present a novel and effective inference approach to conduct both finite- and large-sample inference for high-dimensional linear regression models. This approach is developed under the so-called repro samples framework, in…
The technique of subsampling has been extensively employed to address the challenges posed by limited computing resources and meet the needs for expedite data analysis. Various subsampling methods have been developed to meet the challenges…
High dimensional hypothesis test deals with models in which the number of parameters is significantly larger than the sample size. Existing literature develops a variety of individual tests. Some of them are sensitive to the dense and small…
The Full Bayesian Significance Test (FBST) for precise hypotheses was presented by Pereira and Stern [Entropy 1(4) (1999) 99-110] as a Bayesian alternative instead of the traditional significance test using p-value. The FBST is based on the…
We propose a novel bootstrap test of a dense model, namely factor regression, against a sparse plus dense alternative augmenting model with sparse idiosyncratic components. The asymptotic properties of the test are established under time…
The paper establishes the central limit theorems and proposes how to perform valid inference in factor models. We consider a setting where many counties/regions/assets are observed for many time periods, and when estimation of a global…
Simultaneous variable selection and statistical inference is challenging in high-dimensional data analysis. Most existing post-selection inference methods require explicitly specified regression models, which are often linear, as well as…
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…
The identification of the dependent components in multiple data sets is a fundamental problem in many practical applications. The challenge in these applications is that often the data sets are high-dimensional with few observations or…