arXiv subjects

Jingxiao Zhang

Publications and source records attributed to Jingxiao Zhang.

14 recordsLinked to original sources

arXiv2026

Statistical Inference for Smoothed Support Vector Machines in High Dimensions: From Offline to Online Data

High-dimensional classification problems often rely on the Lasso-penalized linear Support Vector Machines (SVMs). However, the double non-smoothness induced by the hinge loss and Lasso penalty in this model makes statistical inference challenging and impedes computational efficiency. In this paper, we propose a unified inference framework in both offline and online settings. In the offline case, by applying a convolution smoothing technique to the hinge loss, we construct a debiased estimator that eliminates the shrinkage bias, thereby building a valid confidence interval. For online streaming data, we develop a real-time estimator and inference procedure that relies only on summary statistics of historical data. Theoretically, we provide rigorous proofs for the asymptotic normality of our offline and online debiased estimators. Simulation studies and real data applications demonstrate that our methods achieve valid statistical inference and improved computational efficiency.

stat.ME↗

arXiv2026

Successive classification learning for estimating quantile optimal treatment regimes

Quantile optimal treatment regimes (OTRs) aim to assign treatments that maximize a specified quantile of patients' outcomes. Compared to treatment regimes that target the mean outcomes, quantile OTRs offer fairer regimes when a lower quantile is selected, as it improves outcomes for vulnerable patients. In this paper, we propose a novel method for estimating quantile OTRs by reformulating the problem as a successive classification task, solvable via training a sequence of classifiers, each successive classifier built on the output of its predecessors. This reformulation enables us to leverage the powerful machine learning technique to enhance computational efficiency and handle complex decision boundaries. We also investigate the estimation of quantile OTRs when outcomes are discrete, a setting that has received limited attention in the literature. A key challenge is that direct extensions of existing methods to discrete outcomes often lead to inconsistency and ineffectiveness issues. To overcome this, we introduce a smoothing technique that maps discrete outcomes to continuous surrogates, enabling consistent and effective estimation. We provide theoretical guarantees to support our methodology, and demonstrate its superior performance through comprehensive simulation studies and real-data analysis.

stat.ME↗

arXiv2025

Scalable and Distributed Individualized Treatment Rules for Massive Datasets

Synthesizing information from multiple data sources is crucial for constructing accurate individualized treatment rules (ITRs). However, privacy concerns often present significant barriers to the integrative analysis of such multi-source data. Classical meta-learning, which averages local estimates to derive the final ITR, is frequently suboptimal due to biases in these local estimates. To address these challenges, we propose a convolution-smoothed weighted support vector machine for learning the optimal ITR. The accompanying loss function is both convex and smooth, which allows us to develop an efficient multi-round distributed learning procedure for ITRs. Such distributed learning ensures optimal statistical performance with a fixed number of communication rounds, thereby minimizing coordination costs across data centers while preserving data privacy. Our method avoids pooling subject-level raw data and instead requires only sharing summary statistics. Additionally, we develop an efficient coordinate gradient descent algorithm, which guarantees at least linear convergence for the resulting optimization problem. Extensive simulations and an application to sepsis treatment across multiple intensive care units validate the effectiveness of the proposed method.

stat.ME↗

arXiv2025

Doubly robust estimation of optimal treatment regimes for survival data using an instrumental variable

In survival contexts, substantial literature exists on estimating optimal treatment regimes, where treatments are assigned based on personal characteristics to maximize the survival probability. These methods assume that a set of covariates is sufficient to deconfound the treatment-outcome relationship. However, this assumption can be limited in observational studies or randomized trials in which non-adherence occurs. Therefore, we propose a novel approach to estimating optimal treatment regimes when certain confounders are unobservable and a binary instrumental variable is available. Specifically, via a binary instrumental variable, we propose a semiparametric estimator for optimal treatment regimes by maximizing a Kaplan-Meier-like estimator of the survival function. Furthermore, to increase resistance to model misspecification, we construct novel doubly robust estimators. Since the estimators of the survival function are jagged, we incorporate kernel smoothing methods to improve performance. Under appropriate regularity conditions, the asymptotic properties are rigorously established. Moreover, the finite sample performance is evaluated through simulation studies. Finally, we illustrate our method using data from the National Cancer Institute's prostate, lung, colorectal, and ovarian cancer screening trial.

stat.ME↗

arXiv2023

Nonlinear Functional Principal Component Analysis Using Neural Networks

Functional principal component analysis (FPCA) is an important technique for dimension reduction in functional data analysis (FDA). Classical FPCA method is based on the Karhunen-Loève expansion, which assumes a linear structure of the observed functional data. However, the assumption may not always be satisfied, and the FPCA method can become inefficient when the data deviates from the linear assumption. In this paper, we propose a novel FPCA method that is suitable for data with a nonlinear structure by neural network approach. We construct networks that can be applied to functional data and explore the corresponding universal approximation property. The main use of our proposed nonlinear FPCA method is curve reconstruction. We conduct a simulation study to evaluate the performance of our method. The proposed method is also applied to two real-world data sets to further demonstrate its superiority.

stat.ME↗

arXiv2023

Model Averaging by Cross-validation for Partially Linear Functional Additive Models

In this paper, we propose a model averaging approach for addressing model uncertainty in the context of partial linear functional additive models. These models are designed to describe the relation between a response and mixed-types of predictors by incorporating both the parametric effect of scalar variables and the additive effect of a functional variable. The proposed model averaging scheme assigns weights to candidate models based on the minimization of a multi-fold cross-validation criterion. Furthermore, we establish the asymptotic optimality of the resulting estimator in terms of achieving the lowest possible square prediction error loss under model misspecification. Extensive simulation studies and an application to a near infrared spectra dataset are presented to support and illustrate our method.

stat.ME↗

arXiv2023

Kernel partial least squares regression for functional nonlinear models

Functional regression is very crucial in functional data analysis and a linear relationship between scalar response and functional predictor is often assumed. However, the linear assumption may not hold in practice, which makes the methods for linear models invalid. To gain more flexibility, we focus on functional nonlinear models and aim to develop new method that requires no strict constraint on the nonlinear structure. Inspired by the idea of the kernel method in machine learning, we propose a kernel functional partial least squares (KFPLS) method for the functional nonlinear models. The innovative algorithm works on the prediction of the scalar response and is accompanied by R package KFPLS for implementation. The simulation study demonstrates the effectiveness of the proposed method for various types of nonlinear models. Moreover, the real world application also shows the superiority of the proposed KFPLS method.

stat.ME↗

arXiv2022

Partial Replacement Imputation Estimation Method for Complex Missing Covariates in Additive Partially Linear Models

Missing data is a common problem in clinical data collection, which causes difficulty in the statistical analysis of such data. In this article, we consider the problem under a framework of a semiparametric partially linear model when observations are subject to missingness with complex patterns. If the correct model structure of the additive partially linear model is available, we propose to use a new imputation method called Partial Replacement IMputation Estimation (PRIME), which can overcome problems caused by incomplete data in the partially linear model. Also, we use PRIME in conjunction with model averaging (PRIME-MA) to tackle the problem of unknown model structure in the partially linear model. In simulation studies, we use various error distributions, sample sizes, missing data rates, covariate correlations, and noise levels, and PRIME outperforms other methods in almost all cases. With an unknown correct model structure, PRIME-MA has satisfactory performance in terms of prediction, while slightly worse than PRIME. Moreover, we conduct a study of influential factors in Pima Indians Diabetes data, which shows that our method performs better than the other models.

stat.ME↗

arXiv2022

Locally sparse estimator of generalized varying coefficient model for asynchronous longitudinal data

In longitudinal study, it is common that response and covariate are not measured at the same time, which complicates the analysis to a large extent. In this paper, we take into account the estimation of generalized varying coefficient model with such asynchronous observations. A penalized kernel-weighted estimating equation is constructed through kernel technique in the framework of functional data analysis. Moreover, local sparsity is also considered in the estimating equation to improve the interpretability of the estimate. We extend the iteratively reweighted least squares (IRLS) algorithm in our computation. The theoretical properties are established in terms of both consistency and sparsistency, and the simulation studies further verify the satisfying performance of our method when compared with existing approaches. The method is applied to an AIDS study to reveal its practical merits.

stat.ME↗

arXiv2021

Sparse logistic functional principal component analysis for binary data

Functional binary datasets occur frequently in real practice, whereas discrete characteristics of the data can bring challenges to model estimation. In this paper, we propose a sparse logistic functional principal component analysis (SLFPCA) method to handle the functional binary data. The SLFPCA looks for local sparsity of the eigenfunctions to obtain convenience in interpretation. We formulate the problem through a penalized Bernoulli likelihood with both roughness penalty and sparseness penalty terms. An efficient algorithm is developed for the optimization of the penalized likelihood using majorization-minimization (MM) algorithm. The theoretical results indicate both consistency and sparsistency of the proposed method. We conduct a thorough numerical experiment to demonstrate the advantages of the SLFPCA approach. Our method is further applied to a physical activity dataset.

stat.ME↗

arXiv2021

Functional principal component analysis estimator for non-Gaussian data

Functional principal component analysis (FPCA) could become invalid when data involve non-Gaussian features. Therefore, we aim to develop a general FPCA method to adapt to such non-Gaussian cases. A Kenall's $τ$ function, which possesses identical eigenfunctions as covariance function, is constructed. The particular formulation of Kendall's $τ$ function makes it less insensitive to data distribution. We further apply it to the estimation of FPCA and study the corresponding asymptotic consistency. Moreover, the effectiveness of the proposed method is demonstrated through a comprehensive simulation study and an application to the physical activity data collected by a wearable accelerometer monitor.

stat.ME↗

arXiv2021

Projective Resampling Imputation Mean Estimation Method for Missing Covariates Problem

Missing data is a common problem in clinical data collection, which causes difficulty in the statistical analysis of such data. To overcome problems caused by incomplete data, we propose a new imputation method called projective resampling imputation mean estimation (PRIME), which can also address ``the curse of dimensionality" problem in imputation with less information loss. We use various sample sizes, missing-data rates, covariate correlations, and noise levels in simulation studies, and all results show that PRIME outperformes other methods such as iterative least-squares estimation (ILSE), maximum likelihood (ML), and complete-case analysis (CC). Moreover, we conduct a study of influential factors in cardiac surgery-associated acute kidney injury (CSA-AKI), which show that our method performs better than the other models. Finally, we prove that PRIME has a consistent property under some regular conditions.

stat.ME↗

arXiv2021

Model Averaging Estimation for Partially Linear Functional Score Models

This paper is concerned with model averaging estimation for partially linear functional score models. These models predict a scalar response using both parametric effect of scalar predictors and non-parametric effect of a functional predictor. Within this context, we develop a Mallows-type criterion for choosing weights. The resulting model averaging estimator is proved to be asymptotically optimal under certain regularity conditions in terms of achieving the smallest possible squared error loss. Simulation studies demonstrate its superiority or comparability to information criterion score-based model selection and averaging estimators. The proposed procedure is also applied to two real data sets for illustration. That the components of nonparametric part are unobservable leads to a more complicated situation than ordinary partially linear models (PLM) and a different theoretical derivation from those of PLM.

stat.ME↗

arXiv2021

Robust Functional Principal Component Analysis for Non-Gaussian Longitudinal Data

Functional principal component analysis is essential in functional data analysis, but the inferences will become unconvincing when some non-Gaussian characteristics occur, such as heavy tail and skewness. The focus of this paper is to develop a robust functional principal component analysis methodology in dealing with non-Gaussian longitudinal data, for which sparsity and irregularity along with non-negligible measurement errors must be considered. We introduce a Kendall's $τ$ function whose particular properties make it a nice proxy for the covariance function in the eigenequation when handling non-Gaussian cases. Moreover, the estimation procedure is presented and the asymptotic theory is also established. We further demonstrate the superiority and robustness of our method through simulation studies and apply the method to the longitudinal CD4 cell count data in an AIDS study.

stat.ME↗