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3. Non-iterative Gaussianization

Author

Rui, Rongxiang and Tian, Maozai

Subjects
Statistics - Methodology, Statistics - Other Statistics
Abstract

In this work, we propose a non-iterative Gaussian transformation strategy based on copula function, which doesn't require some commonly seen restrictive assumptions in the previous studies such as the elliptically symmetric distribution assumption and the linear independent component analysis assumption. Theoretical properties guarantee the proposed strategy can exactly transfer any random variable vector with a continuous multivariate distribution to a variable vector that follows a multivariate Gaussian distribution. Simulation studies also demonstrate the outperformance of such a strategy compared to some other methods like Box-Cox Gaussianization and radial Gaussianization. An application for probability density estimation for image synthesis is also shown., Comment: 26 pages, 5 figures

Published
2022

6. Communication-Efficient Distributed Estimator for Generalized Linear Models with a Diverging Number of Covariates

Author

Zhou, Ping, Yu, Zhen, Ma, Jingyi, Tian, Maozai, and Fan, Ye

Subjects
Statistics - Methodology, Computer Science - Distributed, Parallel, and Cluster Computing, Computer Science - Machine Learning, Statistics - Machine Learning
Abstract

Distributed statistical inference has recently attracted immense attention. The asymptotic efficiency of the maximum likelihood estimator (MLE), the one-step MLE, and the aggregated estimating equation estimator are established for generalized linear models under the "large $n$, diverging $p_n$" framework, where the dimension of the covariates $p_n$ grows to infinity at a polynomial rate $o(n^\alpha)$ for some $0<\alpha<1$. Then a novel method is proposed to obtain an asymptotically efficient estimator for large-scale distributed data by two rounds of communication. In this novel method, the assumption on the number of servers is more relaxed and thus practical for real-world applications. Simulations and a case study demonstrate the satisfactory finite-sample performance of the proposed estimators.

Published
2020

11. Interpretable Machine Learning-Based Influence Factor Identification for 3D Printing Process–Structure Linkages.

Author

Liu, Fuguo, Chen, Ziru, Xu, Jun, Zheng, Yanyan, Su, Wenyi, Tian, Maozai, and Li, Guodong

Subjects
RAPID prototyping, THREE-dimensional printing, DECISION trees, RANDOM forest algorithms, ELASTIC modulus, BOOSTING algorithms, MACHINE learning
Abstract

Three-dimensional printing technology is a rapid prototyping technology that has been widely used in manufacturing. However, the printing parameters in the 3D printing process have an important impact on the printing effect, so these parameters need to be optimized to obtain the best printing effect. In order to further understand the impact of 3D printing parameters on the printing effect, make theoretical explanations from the dimensions of mathematical models, and clarify the rationality of certain important parameters in previous experience, the purpose of this study is to predict the impact of 3D printing parameters on the printing effect by using machine learning methods. Specifically, we used four machine learning algorithms: SVR (support vector regression): A regression method that uses the principle of structural risk minimization to find a hyperplane in a high-dimensional space that best fits the data, with the goal of minimizing the generalization error bound. Random forest: An ensemble learning method that constructs a multitude of decision trees and outputs the class that is the mode of the classes (classification) or mean prediction (regression) of the individual trees. GBDT (gradient boosting decision tree): An iterative ensemble technique that combines multiple weak prediction models (decision trees) into a strong one by sequentially minimizing the loss function. Each subsequent tree is built to correct the errors of the previous tree. XGB (extreme gradient boosting): An optimized and efficient implementation of gradient boosting that incorporates various techniques to improve the performance of gradient boosting frameworks, such as regularization and sparsity-aware splitting algorithms. The influence of the print parameters on the results under the feature importance and SHAP (Shapley additive explanation) values is compared to determine which parameters have the greatest impact on the print effect. We also used feature importance and SHAP values to compare the importance impact of print parameters on results. In the experiment, we used a dataset with multiple parameters and divided it into a training set and a test set. Through Bayesian optimization and grid search, we determined the best hyperparameters for each algorithm and used the best model to make predictions for the test set. We compare the predictive performance of each model and confirm that the extrusion expansion ratio, elastic modulus, and elongation at break have the greatest influence on the printing effect, which is consistent with the experience. In future, we will continue to delve into methods for optimizing 3D printing parameters and explore how interpretive machine learning can be applied to the 3D printing process to achieve more efficient and reliable printing results. [ABSTRACT FROM AUTHOR]

Published
2024
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12. Quantile Regression for Partially Linear Varying Coefficient Spatial Autoregressive Models

Author

Dai, Xiaowen, Li, Shaoyang, and Tian, Maozai

Subjects
Statistics - Methodology
Abstract

This paper considers the quantile regression approach for partially linear spatial autoregressive models with possibly varying coefficients. B-spline is employed for the approximation of varying coefficients. The instrumental variable quantile regression approach is employed for parameter estimation. The rank score tests are developed for hypotheses on the coefficients, including the hypotheses on the non-varying coefficients and the constancy of the varying coefficients. The asymptotic properties of the proposed estimators and test statistics are both established. Monte Carlo simulations are conducted to study the finite sample performance of the proposed method. Analysis of a real data example is presented for illustration., Comment: 27 pages, 4 figures

Published
2016

13. Quantile Regression for General Spatial Panel Data Models with Fixed Effects

Author

Dai, Xiaowen, Yan, Zhen, Tian, Maozai, and Tang, Manlai

Subjects
Statistics - Methodology
Abstract

This paper considers the quantile regression model with both individual fixed effect and time period effect for general spatial panel data. Instrumental variable quantile regression estimators will be proposed. Asymptotic properties of the proposed estimators will be developed. Simulations are conducted to study the performance of the proposed method. We will illustrate our methodologies using a cigarettes demand data set., Comment: 22 pages, 1 figure

Published
2016

22. Case clustering, contact stratification, and transmission heterogeneity of SARS-CoV-2 Omicron BA.5 variants in Urumqi, China: An observational study

Author

Lu, Yaoqin, primary, Guo, Zihao, additional, Zeng, Ting, additional, Sun, Shengzhi, additional, Lu, Yanmei, additional, Teng, Zhidong, additional, Tian, Maozai, additional, Wang, Jun, additional, Li, Shulin, additional, Fan, Xucheng, additional, Luan, Zemin, additional, Wang, Weiming, additional, Cai, Yongli, additional, Wang, Kai, additional, and Zhao, Shi, additional

Published
2023
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25. Sampling Importance Resampling Algorithm with Nonignorable Missing Response Variable Based on Smoothed Quantile Regression

Author

Guo, Jingxuan, Liu, Fuguo, Härdle, Wolfgang Karl, Zhang, Xueliang, Wang, Kai, Zeng, Ting, Yang, Liping, Tian, Maozai, Guo, Jingxuan, Liu, Fuguo, Härdle, Wolfgang Karl, Zhang, Xueliang, Wang, Kai, Zeng, Ting, Yang, Liping, and Tian, Maozai

Abstract

The presence of nonignorable missing response variables often leads to complex conditional distribution patterns that cannot be effectively captured through mean regression. In contrast, quantile regression offers valuable insights into the conditional distribution. Consequently, this article places emphasis on the quantile regression approach to address nonrandom missing data. Taking inspiration from fractional imputation, this paper proposes a novel smoothed quantile regression estimation equation based on a sampling importance resampling (SIR) algorithm instead of nonparametric kernel regression methods. Additionally, we present an augmented inverse probability weighting (AIPW) smoothed quantile regression estimation equation to reduce the influence of potential misspecification in a working model. The consistency and asymptotic normality of the empirical likelihood estimators corresponding to the above estimating equations are proven under the assumption of a correctly specified parameter working model. Furthermore, we demonstrate that the AIPW estimation equation converges to an IPW estimation equation when a parameter working model is misspecified, thus illustrating the robustness of the AIPW estimation approach. Through numerical simulations, we examine the finite sample properties of the proposed method when the working models are both correctly specified and misspecified. Furthermore, we apply the proposed method to analyze HIV—CD4 data, thereby exploring variations in treatment effects and the influence of other covariates across different quantiles., Fundamental Research Funds for the Central Universities and the Research Funds of Renmin University of China, Peer Reviewed

Published
2023

26. Weighted Competing Risks Quantile Regression Models and Variable Selection

Author

Zhan, Yiqiang, Liu, Xingrong, Li, Erqian, Pan, Jianxin, Tang, Manlai, Yu, Keming, Härdle, Wolfgang Karl, Dai, Xiaowen, Tian, Maozai, Zhan, Yiqiang, Liu, Xingrong, Li, Erqian, Pan, Jianxin, Tang, Manlai, Yu, Keming, Härdle, Wolfgang Karl, Dai, Xiaowen, and Tian, Maozai

Abstract

The proportional subdistribution hazards (PSH) model is popularly used to deal with competing risks data. Censored quantile regression provides an important supplement as well as variable selection methods due to large numbers of irrelevant covariates in practice. In this paper, we study variable selection procedures based on penalized weighted quantile regression for competing risks models, which is conveniently applied by researchers. Asymptotic properties of the proposed estimators, including consistency and asymptotic normality of non-penalized estimator and consistency of variable selection, are established. Monte Carlo simulation studies are conducted, showing that the proposed methods are considerably stable and efficient. Real data about bone marrow transplant (BMT) are also analyzed to illustrate the application of the proposed procedure., National Natural Science Foundation of China, Scientific Research Foundation of North China University of Technology, Fundamental Research Funds for Beijing Universities, NCUT, National Natural Science Foundation of China, China Statistical Research Project, Peer Reviewed

Published
2023

37. Relationship Analysis of Inorganic Arsenic Exposure and Metabolic Syndrome Based on Propensity Score Matching in Xinjiang, China

Author

Nie,Yanwu, Wang,Chenchen, Yang,Lei, Yang,Zhen, Sun,Yahong, Tian,Maozai, Ma,Yuhua, Zhang,Yuxia, Yuan,Yimu, Zhang,Liping, Nie,Yanwu, Wang,Chenchen, Yang,Lei, Yang,Zhen, Sun,Yahong, Tian,Maozai, Ma,Yuhua, Zhang,Yuxia, Yuan,Yimu, and Zhang,Liping

Abstract

Yanwu Nie,1,&ast; Chenchen Wang,2,&ast; Lei Yang,3 Zhen Yang,4 Yahong Sun,4 Maozai Tian,5,6 Yuhua Ma,7,8 Yuxia Zhang,9 Yimu Yuan,10 Liping Zhang6 1State Key Laboratory of Pathogenesis, Prevention and Treatment of High Incidence Diseases in Central Asia, School of Public Health, Xinjiang Medical University, Urumqi, 830017, People’s Republic of China; 2Center for Disease Control and prevention of Xinjiang Uygur Autonomous Region, Urumqi, 830017, People’s Republic of China; 3School of Nursing, Xinjiang Medical University, Urumqi, 830017, People’s Republic of China; 4School of Public Health, Xinjiang Medical University, Urumqi, 830017, People’s Republic of China; 5Center for Applied Statistics, School of Statistics, Renmin University of China, Beijing, 100872, People’s Republic of China; 6College of Medical Engineering and Technology, Xinjiang Medical University, Urumqi, 830017, People’s Republic of China; 7Department of Oncology, Shanghai East Hospital, Tongji University School of Medicine, Shanghai, 200120, People’s Republic of China; 8Department of Pathology, Karamay Central Hospital of XinJiang Karamay, Karamay, Xinjiang Uygur Autonomous Region, 834000, People’s Republic of China; 9Department of Clinical Nutrition, Urumqi Maternal and Child Health Institute, Urumqi, 830001, People’s Republic of China; 10Department of General Practice Medicine, Xinjiang Corps Hospital, Urumqi, People’s Republic of China&ast;These authors contributed equally to this workCorrespondence: Liping Zhang, Email zhanglp1219@163.comPurpose: The role of inorganic arsenic (iAs) in the risk of metabolic syndrome (MetS) remains unclear. This investigation focused on the effect of iAs exposure on MetS and whether the results are consistent in different subgroups.Patients and Methods: The present study was conducted on 629 men and 616 women aged 35– 70 years and living in Xinjiang Uygur Autonomous Region, China. The 1:1 propensity score matching (PSM) was adopted t

Published
2022

38. Sparse regression for low-dimensional time-dynamic varying coefficient models with application to air quality data.

Author

Liang, Jinwen and Tian, Maozai

Subjects
*AIR quality, *ASYMPTOTIC distribution, *PARAMETERIZATION, *SPLINES
Abstract

Time dynamic varying coefficient models play an important role in applications of biology, medicine, environment, finance, etc. Traditional methods, such as kernel smoothing and spline smoothing, are popular. But explicit expressions are unavailable using these methods, and the convergence rate of coefficient function estimators is slow. To address these problems, we expand the varying component with appropriate basis functions. And then we solve a sparse regression problem via a sequential thresholded least-squares estimator. The "parameterization" leads to explicit expressions and fast computation speed. Convergence of the sequential thresholded least squares algorithm is guaranteed. The asymptotic distribution of the coefficient function estimator is derived under certain assumptions. Our simulation shows the proposed method has higher precision and computing speed. Finally, our proposed method is applied to the study of PM 2.5 concentration in Beijing. We analyze the relationship between PM 2.5 and other impact factors. [ABSTRACT FROM AUTHOR]

Published
2023
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49. Penalized weigted competing risks models based on quantile regression

Author

Li, Erqian, Härdle, Wolfgang, Dai, Xiaowen, and Tian, Maozai

Subjects
Statistics::Theory, Cumulative incidence function, Kaplan-Meier estimator, ddc:330, Statistics::Methodology, Redistribution method, Competing risks, C00, Statistics::Computation
Abstract

The proportional subdistribution hazards (PSH) model is popularly used to deal with competing risks data. Censored quantile regression provides an important supplement as well as variable selection methods, due to large numbers of irrelevant covariates in practice. In this paper, we study variable selection procedures based on penalized weighted quantile regression for competing risks models, which is conveniently applied by researchers. Asymptotic properties of the proposed estimators including consistency and asymptotic normality of non-penalized estimator and consistency of variable selection are established. Monte Carlo simulation studies are conducted, showing that the proposed methods are considerably stable and efficient. A real data about bone marrow transplant (BMT) is also analyzed to illustrate the application of proposed procedure.

Published
2021

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