arXiv subjects

Lianqiang Qu

Publications and source records attributed to Lianqiang Qu.

10 recordsLinked to original sources

arXiv2026

Causal inference for censored data with continuous marks

This paper presents a framework for causal inference in the presence of censored data,where the failure time is marked by a continuous variable referred to as a mark.The mark is observed after treatment and is not meaningful when the failure time is censored. In addition, due to the continuous nature of the marks, observations at each given mark are sparse. These facts make the identification and estimation of causality a challenging task. To address these issues, we define a new mark-specific treatment effect within the potential outcomes framework and characterize its identifying conditions. We then propose a local smoothing estimator for the causal effects and establish its asymptotic properties. We further develop testing methods to evaluate whether the treatment has an effect on the failure time when controlling the values of the mark at certain points or within a defined interval, and develop a Gaussian approximation method to obtain the critical values. We evaluate our method using simulation studies as well as a real dataset from the Antibody Mediated Prevention trials.

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arXiv2026

Semiparametric analysis for paired comparisons with covariates

Statistical inference in parametric models (e.g., the Bradley--Terry model and its variants) for paired-comparison data has been explored in the high-dimensional regime, in which the number of items involving in paired comparisons diverges. However, parametric models are highly susceptible to model misspecification. To relax the assumption of known distributions and provide flexibility, we propose a semiparametric framework for modeling the merits of items and covariate effects (e.g., home-field advantage) by introducing latent random variables with unspecified distributions. As the number of parameters increases with the number of items, semiparametric inference is highly nontrivial. To address this issue, we employ a kernel-based least squares approach to estimate all unknown parameters. When each pair of items has a fixed number of comparisons and the number of items tends to infinity, we prove the consistency of all resulting estimators and derive their asymptotic normal distributions. To the best of our knowledge, this is the first study to conduct a semiparametric analysis of paired comparisons with an increasing dimension. We conduct simulations to evaluate the finite-sample performance of the proposed method and illustrate its practical utility by analyzing an NBA dataset.

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arXiv2025

Conditional inference for high-dimensional multi-omics survival data

Multi-omics data present significant challenges for statistical inference due to the complex interdependencies among biological layers. In this paper, we introduce a novel Multi-Omics Factor-Adjusted Cox (MOFA-Cox) model for analyzing multi-omics survival data, effectively addressing the intricate correlations across various omics layers. We provide a factor-adjusted decorrelated score test for the MOFA-Cox model in high-dimensional survival analysis. Our method accommodates situations where the dimension of the parameters being tested exceeds the sample size, while not imposing a sparsity assumption on them. We establish the limiting null distribution of the proposed test and analyze its power under local alternatives. Numerical studies and an application to the TCGA breast cancer dataset demonstrate the effectiveness of our method.

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arXiv2025

Temporal network analysis via a degree-corrected Cox model

Temporal dynamics, characterised by time-varying degree heterogeneity and homophily effects, are often exhibited in many real-world networks. As observed in an MIT Social Evolution study, the in-degree and out-degree of the nodes show considerable heterogeneity that varies with time. Concurrently, homophily effects, which explain why nodes with similar characteristics are more likely to connect with each other, are also time-dependent. To facilitate the exploration and understanding of these dynamics, we propose a novel degree-corrected Cox model for directed networks, where the way for degree-heterogeneity or homophily effects to change with time is left completely unspecified. Because each node has individual-specific in- and out-degree parameters that vary over time, the number of unknown parameters grows with the number of nodes, leading to a high-dimensional estimation problem. Therefore, it is highly nontrivial to make inference. We develop a local estimating equations approach to estimate the unknown parameters and establish the consistency and asymptotic normality of the proposed estimators in the high-dimensional regime. We further propose test statistics to check whether temporal variation or degree heterogeneity is present in the network and develop a graphically diagnostic method to evaluate goodness-of-fit for dynamic network models. Simulation studies and two real data analyses are provided to assess the finite sample performance of the proposed method and illustrate its practical utility.

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arXiv2025

Inference in semiparametric formation models for directed networks

We propose a semiparametric model for dyadic link formations in directed networks. The model contains a set of degree parameters that measure different effects of popularity or outgoingness across nodes, a regression parameter vector that reflects the homophily effect resulting from the nodal attributes or pairwise covariates associated with edges, and a set of latent random noises with unknown distributions. Our interest lies in inferring the unknown degree parameters and homophily parameters. The dimension of the degree parameters increases with the number of nodes. Under the high-dimensional regime, we develop a kernel-based least squares approach to estimate the unknown parameters. The major advantage of our estimator is that it does not encounter the incidental parameter problem for the homophily parameters. We prove consistency of all the resulting estimators of the degree parameters and homophily parameters. We establish high-dimensional central limit theorems for the proposed estimators and provide several applications of our general theory, including testing the existence of degree heterogeneity, testing sparse signals and recovering the support. Simulation studies and a real data application are conducted to illustrate the finite sample performance of the proposed methods.

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arXiv2025

Maximum likelihood estimation in the sparse Rasch model

The Rasch model has been widely used to analyse item response data in psychometrics and educational assessments. When the number of individuals and items are large, it may be impractical to provide all possible responses. It is desirable to study sparse item response experiments. Here, we propose to use the Erdős\textendash Rényi random sampling design, where an individual responds to an item with low probability $p$. We prove the uniform consistency of the maximum likelihood estimator %by developing a leave-one-out method for the Rasch model when both the number of individuals, $r$, and the number of items, $t$, approach infinity. Sampling probability $p$ can be as small as $\max\{\log r/r, \log t/t\}$ up to a constant factor, which is a fundamental requirement to guarantee the connection of the sampling graph by the theory of the Erdős\textendash Rényi graph. The key technique behind this significant advancement is a powerful leave-one-out method for the Rasch model. We further establish the asymptotical normality of the MLE by using a simple matrix to approximate the inverse of the Fisher information matrix. The theoretical results are corroborated by simulation studies and an analysis of a large item-response dataset.

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arXiv2024

Linear spline index regression model: Interpretability, nonlinearity and dimension reduction

Inspired by the complexity of certain real-world datasets, this article introduces a novel flexible linear spline index regression model. The model posits piecewise linear effects of an index on the response, with continuous changes occurring at knots. Significantly, it possesses the interpretability of linear models, captures nonlinear effects similar to nonparametric models, and achieves dimension reduction like single-index models. In addition, the locations and number of knots remain unknown, which further enhances the adaptability of the model in practical applications. We propose a new method that combines penalized approaches and convolution techniques to simultaneously estimate the unknown parameters and determine the number of knots. Noteworthy is that the proposed method allows the number of knots to diverge with the sample size. We demonstrate that the proposed estimators can identify the number of knots with a probability approaching one and estimate the coefficients as efficiently as if the number of knots is known in advance. We also introduce a procedure to test the presence of knots. Simulation studies and two real datasets are employed to assess the finite sample performance of the proposed method.

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arXiv2024

Distributed variable screening for generalized linear models

In this article, we develop a distributed variable screening method for generalized linear models. This method is designed to handle situations where both the sample size and the number of covariates are large. Specifically, the proposed method selects relevant covariates by using a sparsity-restricted surrogate likelihood estimator. It takes into account the joint effects of the covariates rather than just the marginal effect, and this characteristic enhances the reliability of the screening results. We establish the sure screening property of the proposed method, which ensures that with a high probability, the true model is included in the selected model. Simulation studies are conducted to evaluate the finite sample performance of the proposed method, and an application to a real dataset showcases its practical utility.

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arXiv2023

Time-varying $β$-model for dynamic directed networks

We extend the well-known $β$-model for directed graphs to dynamic network setting, where we observe snapshots of adjacency matrices at different time points. We propose a kernel-smoothed likelihood approach for estimating $2n$ time-varying parameters in a network with $n$ nodes, from $N$ snapshots. We establish consistency and asymptotic normality properties of our kernel-smoothed estimators as either $n$ or $N$ diverges. Our results contrast their counterparts in single-network analyses, where $n\to\infty$ is invariantly required in asymptotic studies. We conduct comprehensive simulation studies that confirm our theory's prediction and illustrate the performance of our method from various angles. We apply our method to an email data set and obtain meaningful results.

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arXiv2023

A degree-corrected Cox model for dynamic networks

Continuous time network data have been successfully modeled by multivariate counting processes, in which the intensity function is characterized by covariate information. However, degree heterogeneity has not been incorporated into the model which may lead to large biases for the estimation of homophily effects. In this paper, we propose a degree-corrected Cox network model to simultaneously analyze the dynamic degree heterogeneity and homophily effects for continuous time directed network data. Since each node has individual-specific in- and out-degree effects in the model, the dimension of the time-varying parameter vector grows with the number of nodes, which makes the estimation problem non-standard. We develop a local estimating equations approach to estimate unknown time-varying parameters, and establish consistency and asymptotic normality of the proposed estimators by using the powerful martingale process theories. We further propose test statistics to test for trend and degree heterogeneity in dynamic networks. Simulation studies are provided to assess the finite sample performance of the proposed method and a real data analysis is used to illustrate its practical utility.

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