arXiv subjects

Cheng Yong Tang

Publications and source records attributed to Cheng Yong Tang.

At least 19 recordsLinked to original sources

arXiv2026

Controlling the false discovery rate in high-dimensional linear models using model-X knockoffs and $p$-values

We propose a novel multiple testing methodology for controlling the false discovery rate (FDR) in high-dimensional linear models that integrates model-X knockoff techniques with debiased penalized regression estimators. At the foundation of our methodology, we construct and study two sets of naturally paired high-dimensional test statistics and the associated $p$-values for evaluating the same null hypotheses. The first set is shown to be asymptotically mutually independent, justifying the use of the Benjamini-Hochberg procedure. We further exploit the pairing structure through a two-step procedure aimed at improving power. Our theoretical results establish the key properties of the framework with respect to asymptotic FDR control and formally characterize the associated power gains of the two-step procedure. Importantly, our framework accommodates general dependence in the design matrix. Extensive simulations demonstrate that our methods outperform existing approaches -- particularly those relying on empirical FDP estimates -- in both power and FDR control accuracy, with notable gains in settings involving weaker signals, small sample sizes, or low target FDR levels.

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arXiv2025

Targeted learning via probabilistic subpopulation matching

In biomedical research, to obtain more accurate prediction results from a target study, leveraging information from multiple similar source studies is proved to be useful. However, in many biomedical applications based on real-world data, populations under consideration in different studies, e.g., clinical sites, can be heterogeneous, leading to challenges in properly borrowing information towards the target study. The state of art methods are typically based on study-level matching to identify source studies that are similar to the target study, whilst samples from source studies that significantly differ from the target study will all be dropped at the study level, which can lead to substantial loss of information. We consider a general situation where all studies are sampled from a super-population composed of distinct subpopulations, and propose a novel framework of targeted learning via subpopulation matching. In contrast to the existing study-level matching methods, measuring similarities between subpopulations can effectively decompose both within- and between-study heterogeneity, allowing incorporation of information from all source studies without dropping any samples as in the existing methods. We devise the proposed framework as a two-step procedure, where a finite mixture model is first fitted jointly across all studies to provide subject-wise probabilistic subpopulation information, followed by a step of within-subpopulation information transferring from source studies to the target study for each identified subpopulation. We establish the non-asymptotic properties of our estimator and demonstrate the ability of our method to improve prediction at the target study via simulation studies.

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arXiv2025

Generalized Correlation Regression for Disentangling Dependence in Clustered Data

Clustered and longitudinal data are pervasive in scientific studies, from prenatal health programs to clinical trials and public health surveillance. Such data often involve non-Gaussian responses--including binary, categorical, and count outcomes--that exhibit complex correlation structures driven by multilevel clustering, covariates, over-dispersion, or zero inflation. Conventional approaches such as mixed-effects models and generalized estimating equations (GEEs) can capture some of these dependencies, but they are often too rigid or impose restrictive assumptions that limit interpretability and predictive performance. We investigate \emph{generalized correlation regression} (GCR), a unified framework that models correlations directly as functions of interpretable covariates while simultaneously estimating marginal means. By applying a generalized $z$-transformation, GCR guarantees valid correlation matrices, accommodates unbalanced cluster sizes, and flexibly incorporates covariates such as time, space, or group membership into the dependence structure. Through applications to modern prenatal care, a longitudinal toenail infection trial, and clustered health count data, we show that GCR not only achieves superior predictive performance over standard methods, but also reveals family-, community-, and individual-level drivers of dependence that are obscured under conventional modeling. These results demonstrate the broad applied value of GCR for analyzing binary, count, and categorical data in clustered and longitudinal settings.

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arXiv2025

Bayesian penalized empirical likelihood and Markov Chain Monte Carlo sampling

In this study, we introduce a novel methodological framework called Bayesian Penalized Empirical Likelihood (BPEL), designed to address the computational challenges inherent in empirical likelihood (EL) approaches. Our approach has two primary objectives: (i) to enhance the inherent flexibility of EL in accommodating diverse model conditions, and (ii) to facilitate the use of well-established Markov Chain Monte Carlo (MCMC) sampling schemes as a convenient alternative to the complex optimization typically required for statistical inference using EL. To achieve the first objective, we propose a penalized approach that regularizes the Lagrange multipliers, significantly reducing the dimensionality of the problem while accommodating a comprehensive set of model conditions. For the second objective, our study designs and thoroughly investigates two popular sampling schemes within the BPEL context. We demonstrate that the BPEL framework is highly flexible and efficient, enhancing the adaptability and practicality of EL methods. Our study highlights the practical advantages of using sampling techniques over traditional optimization methods for EL problems, showing rapid convergence to the global optima of posterior distributions and ensuring the effective resolution of complex statistical inference challenges.

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arXiv2023

Applied Regression Analysis of Correlations for Correlated Data

Correlated data are ubiquitous in today's data-driven society. While regression models for analyzing means and variances of responses of interest are relatively well-developed, the development of these models for analyzing the correlations is largely confined to longitudinal data, a special form of sequentially correlated data. This paper proposes a new method for the analysis of correlations to fully exploit the use of covariates for general correlated data. In a renewed analysis of the Classroom data, a highly unbalanced multilevel clustered data with within-class and within-school correlations, our method reveals informative insights on these structures not previously known. In another analysis of the malaria immune response data in Benin, a longitudinal study with time-dependent covariates where the exact times of the observations are not available, our approach again provides promising new results. At the heart of our approach is a new generalized z-transformation that converts correlation matrices constrained to be positive definite to vectors with unrestricted support, and is order-invariant. These two properties enable us to develop regression analysis incorporating covariates for the modelling of correlations via the use of maximum likelihood.

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arXiv2023

Efficiently handling constraints with Metropolis-adjusted Langevin algorithm

In this study, we investigate the performance of the Metropolis-adjusted Langevin algorithm in a setting with constraints on the support of the target distribution. We provide a rigorous analysis of the resulting Markov chain, establishing its convergence and deriving an upper bound for its mixing time. Our results demonstrate that the Metropolis-adjusted Langevin algorithm is highly effective in handling this challenging situation: the mixing time bound we obtain is superior to the best known bounds for competing algorithms without an accept-reject step. Our numerical experiments support these theoretical findings, indicating that the Metropolis-adjusted Langevin algorithm shows promising performance when dealing with constraints on the support of the target distribution.

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arXiv2022

Optimal covariance matrix estimation for high-dimensional noise in high-frequency data

We consider high-dimensional measurement errors with high-frequency data. Our objective is on recovering the high-dimensional cross-sectional covariance matrix of the random errors with optimality. In this problem, not all components of the random vector are observed at the same time and the measurement errors are latent variables, leading to major challenges besides high data dimensionality. We propose a new covariance matrix estimator in this context with appropriate localization and thresholding, and then conduct a series of comprehensive theoretical investigations of the proposed estimator. By developing a new technical device integrating the high-frequency data feature with the conventional notion of $α$-mixing, our analysis successfully accommodates the challenging serial dependence in the measurement errors. Our theoretical analysis establishes the minimax optimal convergence rates associated with two commonly used loss functions; and we demonstrate with concrete cases when the proposed localized estimator with thresholding achieves the minimax optimal convergence rates. Considering that the variances and covariances can be small in reality, we conduct a second-order theoretical analysis that further disentangles the dominating bias in the estimator. A bias-corrected estimator is then proposed to ensure its practical finite sample performance. We also extensively analyze our estimator in the setting with jumps, and show that its performance is reasonably robust. We illustrate the promising empirical performance of the proposed estimator with extensive simulation studies and a real data analysis.

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arXiv2021

Adjusting the Benjamini-Hochberg method for controlling the false discovery rate in knockoff assisted variable selection

The knockoff-based multiple testing setup of Barber & Candes (2015) for variable selection in multiple regression where sample size is as large as the number of explanatory variables is considered. The method of Benjamini & Hochberg (1995) based on ordinary least squares estimates of the regression coefficients is adjusted to the setup, transforming it to a valid p-value based false discovery rate controlling method not relying on any specific correlation structure of the explanatory variables. Simulations and real data applications show that our proposed method that is agnostic to π0, the proportion of unimportant explanatory variables, and a data-adaptive version of it that uses an estimate of π0 are powerful competitors of the false discovery rate controlling method in Barber & Candes (2015).

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arXiv2021

Pre-processing with Orthogonal Decompositions for High-dimensional Explanatory Variables

Strong correlations between explanatory variables are problematic for high-dimensional regularized regression methods. Due to the violation of the Irrepresentable Condition, the popular LASSO method may suffer from false inclusions of inactive variables. In this paper, we propose pre-processing with orthogonal decompositions (PROD) for the explanatory variables in high-dimensional regressions. The PROD procedure is constructed based upon a generic orthogonal decomposition of the design matrix. We demonstrate by two concrete cases that the PROD approach can be effectively constructed for improving the performance of high-dimensional penalized regression. Our theoretical analysis reveals their properties and benefits for high-dimensional penalized linear regression with LASSO. Extensive numerical studies with simulations and data analysis show the promising performance of the PROD.

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arXiv2020

Missing at Random or Not: A Semiparametric Testing Approach

Practical problems with missing data are common, and statistical methods have been developed concerning the validity and/or efficiency of statistical procedures. On a central focus, there have been longstanding interests on the mechanism governing data missingness, and correctly deciding the appropriate mechanism is crucially relevant for conducting proper practical investigations. The conventional notions include the three common potential classes -- missing completely at random, missing at random, and missing not at random. In this paper, we present a new hypothesis testing approach for deciding between missing at random and missing not at random. Since the potential alternatives of missing at random are broad, we focus our investigation on a general class of models with instrumental variables for data missing not at random. Our setting is broadly applicable, thanks to that the model concerning the missing data is nonparametric, requiring no explicit model specification for the data missingness. The foundational idea is to develop appropriate discrepancy measures between estimators whose properties significantly differ only when missing at random does not hold. We show that our new hypothesis testing approach achieves an objective data oriented choice between missing at random or not. We demonstrate the feasibility, validity, and efficacy of the new test by theoretical analysis, simulation studies, and a real data analysis.

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arXiv2019

High-dimensional empirical likelihood inference

High-dimensional statistical inference with general estimating equations are challenging and remain less explored. In this paper, we study two problems in the area: confidence set estimation for multiple components of the model parameters, and model specifications test. For the first one, we propose to construct a new set of estimating equations such that the impact from estimating the high-dimensional nuisance parameters becomes asymptotically negligible. The new construction enables us to estimate a valid confidence region by empirical likelihood ratio. For the second one, we propose a test statistic as the maximum of the marginal empirical likelihood ratios to quantify data evidence against the model specification. Our theory establishes the validity of the proposed empirical likelihood approaches, accommodating over-identification and exponentially growing data dimensionality. The numerical studies demonstrate promising performance and potential practical benefits of the new methods.

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arXiv2019

High-dimensional Interactions Detection with Sparse Principal Hessian Matrix

In statistical learning framework with regressions, interactions are the contributions to the response variable from the products of the explanatory variables. In high-dimensional problems, detecting interactions is challenging due to combinatorial complexity and limited data information. We consider detecting interactions by exploring their connections with the principal Hessian matrix. Specifically, we propose a one-step synthetic approach for estimating the principal Hessian matrix by a penalized M-estimator. An alternating direction method of multipliers (ADMM) is proposed to efficiently solve the encountered regularized optimization problem. Based on the sparse estimator, we detect the interactions by identifying its nonzero components. Our method directly targets at the interactions, and it requires no structural assumption on the hierarchy of the interaction effects. We show that our estimator is theoretically valid, computationally efficient, and practically useful for detecting the interactions in a broad spectrum of scenarios.

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arXiv2018

Disentangling and Assessing Uncertainties in Multiperiod Corporate Default Risk Predictions

Measuring the corporate default risk is broadly important in economics and finance. Quantitative methods have been developed to predictively assess future corporate default probabilities. However, as a more difficult yet crucial problem, evaluating the uncertainties associated with the default predictions remains little explored. In this paper, we attempt to fill this blank by developing a procedure for quantifying the level of associated uncertainties upon carefully disentangling multiple contributing sources. Our framework effectively incorporates broad information from historical default data, corporates' financial records, and macroeconomic conditions by a) characterizing the default mechanism, and b) capturing the future dynamics of various features contributing to the default mechanism. Our procedure overcomes the major challenges in this large scale statistical inference problem and makes it practically feasible by using parsimonious models, innovative methods, and modern computational facilities. By predicting the marketwide total number of defaults and assessing the associated uncertainties, our method can also be applied for evaluating the aggregated market credit risk level. Upon analyzing a US market data set, we demonstrate that the level of uncertainties associated with default risk assessments is indeed substantial. More informatively, we also find that the level of uncertainties associated with the default risk predictions is correlated with the level of default risks, indicating potential for new scopes in practical applications including improving the accuracy of default risk assessments.

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arXiv2018

A frequency domain analysis of the error distribution from noisy high-frequency data

Data observed at high sampling frequency are typically assumed to be an additive composite of a relatively slow-varying continuous-time component, a latent stochastic process or a smooth random function, and measurement error. Supposing that the latent component is an Itô diffusion process, we propose to estimate the measurement error density function by applying a deconvolution technique with appropriate localization. Our estimator, which does not require equally-spaced observed times, is consistent and minimax rate optimal. We also investigate estimators of the moments of the error distribution and their properties, propose a frequency domain estimator for the integrated volatility of the underlying stochastic process, and show that it achieves the optimal convergence rate. Simulations and a real data analysis validate our analysis.

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arXiv2017

A new scope of penalized empirical likelihood with high-dimensional estimating equations

Statistical methods with empirical likelihood (EL) are appealing and effective especially in conjunction with estimating equations through which useful data information can be adaptively and flexibly incorporated. It is also known in the literature that EL approaches encounter difficulties when dealing with problems having high-dimensional model parameters and estimating equations. To overcome the challenges, we begin our study with a careful investigation on high-dimensional EL from a new scope targeting at estimating a high-dimensional sparse model parameters. We show that the new scope provides an opportunity for relaxing the stringent requirement on the dimensionality of the model parameter. Motivated by the new scope, we then propose a new penalized EL by applying two penalty functions respectively regularizing the model parameters and the associated Lagrange multipliers in the optimizations of EL. By penalizing the Lagrange multiplier to encourage its sparsity, we show that drastic dimension reduction in the number of estimating equations can be effectively achieved without compromising the validity and consistency of the resulting estimators. Most attractively, such a reduction in dimensionality of estimating equations is actually equivalent to a selection among those high-dimensional estimating equations, resulting in a highly parsimonious and effective device for high-dimensional sparse model parameters. Allowing both the dimensionalities of model parameters and estimating equations growing exponentially with the sample size, our theory demonstrates that the estimator from our new penalized EL is sparse and consistent with asymptotically normally distributed nonzero components. Numerical simulations and a real data analysis show that the proposed penalized EL works promisingly.

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arXiv2016

Tuning parameter selection in high dimensional penalized likelihood

Determining how to appropriately select the tuning parameter is essential in penalized likelihood methods for high-dimensional data analysis. We examine this problem in the setting of penalized likelihood methods for generalized linear models, where the dimensionality of covariates p is allowed to increase exponentially with the sample size n. We propose to select the tuning parameter by optimizing the generalized information criterion (GIC) with an appropriate model complexity penalty. To ensure that we consistently identify the true model, a range for the model complexity penalty is identified in GIC. We find that this model complexity penalty should diverge at the rate of some power of $\log p$ depending on the tail probability behavior of the response variables. This reveals that using the AIC or BIC to select the tuning parameter may not be adequate for consistently identifying the true model. Based on our theoretical study, we propose a uniform choice of the model complexity penalty and show that the proposed approach consistently identifies the true model among candidate models with asymptotic probability one. We justify the performance of the proposed procedure by numerical simulations and a gene expression data analysis.

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arXiv2016

Local independence feature screening for nonparametric and semiparametric models by marginal empirical likelihood

We consider an independence feature screening technique for identifying explanatory variables that locally contribute to the response variable in high-dimensional regression analysis. Without requiring a specific parametric form of the underlying data model, our approach accommodates a wide spectrum of nonparametric and semiparametric model families. To detect the local contributions of explanatory variables, our approach constructs empirical likelihood locally in conjunction with marginal nonparametric regressions. Since our approach actually requires no estimation, it is advantageous in scenarios such as the single-index models where even specification and identification of a marginal model is an issue. By automatically incorporating the level of variation of the nonparametric regression and directly assessing the strength of data evidence supporting local contribution from each explanatory variable, our approach provides a unique perspective for solving feature screening problems. Theoretical analysis shows that our approach can handle data dimensionality growing exponentially with the sample size. With extensive theoretical illustrations and numerical examples, we show that the local independence screening approach performs promisingly.

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arXiv2013

Marginal empirical likelihood and sure independence feature screening

We study a marginal empirical likelihood approach in scenarios when the number of variables grows exponentially with the sample size. The marginal empirical likelihood ratios as functions of the parameters of interest are systematically examined, and we find that the marginal empirical likelihood ratio evaluated at zero can be used to differentiate whether an explanatory variable is contributing to a response variable or not. Based on this finding, we propose a unified feature screening procedure for linear models and the generalized linear models. Different from most existing feature screening approaches that rely on the magnitudes of some marginal estimators to identify true signals, the proposed screening approach is capable of further incorporating the level of uncertainties of such estimators. Such a merit inherits the self-studentization property of the empirical likelihood approach, and extends the insights of existing feature screening methods. Moreover, we show that our screening approach is less restrictive to distributional assumptions, and can be conveniently adapted to be applied in a broad range of scenarios such as models specified using general moment conditions. Our theoretical results and extensive numerical examples by simulations and data analysis demonstrate the merits of the marginal empirical likelihood approach.

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