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We develop non-asymptotically justified methods for hypothesis testing about the $p-$dimensional coefficients $\theta^{*}$ in (possibly nonlinear) regression models. Given a function $h:\,\mathbb{R}^{p}\mapsto\mathbb{R}^{m}$, we consider…
This paper deals with the asymptotic statistical properties of a class of redescending M-estimators in linear models with increasing dimension. This class is wide enough to include popular high breakdown point estimators such as…
When testing for the mean vector in a high dimensional setting, it is generally assumed that the observations are independently and identically distributed. However if the data are dependent, the existing test procedures fail to preserve…
This paper investigates the high-dimensional linear regression with highly correlated covariates. In this setup, the traditional sparsity assumption on the regression coefficients often fails to hold, and consequently many model selection…
Misspecified models often provide useful information about the true data generating distribution. For example, if $y$ is a non-linear function of $x$ the least squares estimator $\hat{\beta}$ is an estimate of $\beta$, the slope of the best…
An important question in statistical network analysis is how to estimate models of discrete and dependent network data with intractable likelihood functions, without sacrificing computational scalability and statistical guarantees. We…
High-dimensional vector autoregression with measurement error is frequently encountered in a large variety of scientific and business applications. In this article, we study statistical inference of the transition matrix under this model.…
We propose two semiparametric versions of the debiased Lasso procedure for the model $Y_i = X_i\beta_0 + g_0(Z_i) + \epsilon_i$, where $\beta_0$ is high dimensional but sparse (exactly or approximately). Both versions are shown to have the…
In semi-supervised learning, the prevailing understanding suggests that observing additional unlabeled samples improves estimation accuracy for linear parameters only in the case of model misspecification. In this work, we challenge such a…
Statistical inferences for high-dimensional regression models have been extensively studied for their wide applications ranging from genomics, neuroscience, to economics. However, in practice, there are often potential unmeasured…
In this paper, we investigate the adequacy testing problem of high-dimensional factor-augmented regression model. Existing test procedures perform not well under dense alternatives. To address this critical issue, we introduce a novel…
In this paper, we introduce an innovative testing procedure for assessing individual hypotheses in high-dimensional linear regression models with measurement errors. This method remains robust even when either the X-model or Y-model is…
This paper develops an inferential theory for high-dimensional matrix-variate factor models with missing observations. We propose an easy-to-use all-purpose method that involves two straightforward steps. First, we perform principal…
This paper aims to develop an effective model-free inference procedure for high-dimensional data. We first reformulate the hypothesis testing problem via sufficient dimension reduction framework. With the aid of new reformulation, we…
Linear models are foundational tools in statistics and ubiquitous across the applied sciences. However, conventional statistical inference -- such as $t$-tests and $F$-tests -- are only valid at fixed sample sizes, making them unsuitable…
We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…
We consider the high-dimensional linear regression model $Y = X \beta^0 + \epsilon$ with Gaussian noise $\epsilon$ and Gaussian random design $X$. We assume that $\Sigma:= E X^T X / n$ is non-singular and write its inverse as $\Theta :=…
We develop inference procedures robust to general forms of weak dependence. The procedures utilize test statistics constructed by resampling in a manner that does not depend on the unknown correlation structure of the data. We prove that…
Model selection criteria are one of the most important tools in statistics. Proofs showing a model selection criterion is asymptotically optimal are tailored to the type of model (linear regression, quantile regression, penalized…
We present improved methods for calculating confidence intervals and $p$-values in situations where standard asymptotic approaches fail due to small sample sizes. We apply these techniques to a specific class of statistical model that can…