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学者姓名：程维虎
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Abstract ：
In this study, the authors proposed upper tolerance limits for the gamma mixture distribution based on generalized fiducial inference, and an MCMC simulation is performed to sample from the generalized fiducial distributions. The simulation results and a real hydrological data example show that the proposed tolerance limits are more efficient.
Keyword ：
Markov chain Monte Carlo Markov chain Monte Carlo incomplete data incomplete data latent variable latent variable generalized fiducial inference generalized fiducial inference Gamma mixture distribution Gamma mixture distribution
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| GB/T 7714 | Jiao, Junjun , Cheng, Weihu . Tolerance Limits Under Gamma Mixtures: Application in Hydrology [J]. | JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY , 2023 , 36 (3) : 1285-1301 . |
| MLA | Jiao, Junjun 等. "Tolerance Limits Under Gamma Mixtures: Application in Hydrology" . | JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY 36 . 3 (2023) : 1285-1301 . |
| APA | Jiao, Junjun , Cheng, Weihu . Tolerance Limits Under Gamma Mixtures: Application in Hydrology . | JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY , 2023 , 36 (3) , 1285-1301 . |
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Abstract ：
In estimating logistic regression models, convergence of the maximization algorithm is critical; however, this may fail. Numerous bias correction methods for maximum likelihood estimates of parameters have been conducted for cases of complete data sets, and also for longitudinal models. Balanced data sets yield consistent estimates from conditional logit estimators for binary response panel data models. When faced with a missing covariates problem, researchers adopt various imputation techniques to complete the data and without loss of generality; consistent estimates still suffice asymptotically. For maximum likelihood estimates of the parameters for logistic regression in cases of imputed covariates, the optimal choice of an imputation technique that yields the best estimates with minimum variance is still elusive. This paper aims to examine the behaviour of the Hessian matrix with optimal values of the imputed covariates vector, which will make the Newton-Raphson algorithm converge faster through a reduced absolute value of the product of the score function and the inverse fisher information component. We focus on a method used to modify the conditional likelihood function through the partitioning of the covariate matrix. We also confirm that the positive moduli of the Hessian for conditional estimators are sufficient for the concavity of the log-likelihood function, resulting in optimum parameter estimates. An increased Hessian modulus ensures the faster convergence of the parameter estimates. Simulation results reveal that model-based imputations perform better than classical imputation techniques, yielding estimates with smaller bias and higher precision for the conditional maximum likelihood estimation of nonlinear panel models.
Keyword ：
Hessian matrix Hessian matrix fixed effects fixed effects maximum likelihood maximum likelihood conditional logit conditional logit
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| GB/T 7714 | Otieno, Opeyo Peter , Cheng, Weihu . The Concavity of Conditional Maximum Likelihood Estimation for Logit Panel Data Models with Imputed Covariates [J]. | MATHEMATICS , 2023 , 11 (20) . |
| MLA | Otieno, Opeyo Peter 等. "The Concavity of Conditional Maximum Likelihood Estimation for Logit Panel Data Models with Imputed Covariates" . | MATHEMATICS 11 . 20 (2023) . |
| APA | Otieno, Opeyo Peter , Cheng, Weihu . The Concavity of Conditional Maximum Likelihood Estimation for Logit Panel Data Models with Imputed Covariates . | MATHEMATICS , 2023 , 11 (20) . |
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Abstract ：
In this paper, we propose a model averaging estimation for the varying-coefficient partially linear models with missing responses. Within this context, we construct a HRCp weight choice criterion that exhibits asymptotic optimality under certain assumptions. Our model averaging procedure can simultaneously address the uncertainty on which covariates to include and the uncertainty on whether a covariate should enter the linear or nonlinear component of the model. The simulation results in comparison with some related strategies strongly favor our proposal. A real dataset is analyzed to illustrate the practical application as well.
Keyword ：
model averaging model averaging HRCp HRCp asymptotic optimality asymptotic optimality missing data missing data varying-coefficient partially linear model varying-coefficient partially linear model
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| GB/T 7714 | Zeng, Jie , Cheng, Weihu , Hu, Guozhi . Optimal Model Averaging Estimation for the Varying-Coefficient Partially Linear Models with Missing Responses [J]. | MATHEMATICS , 2023 , 11 (8) . |
| MLA | Zeng, Jie 等. "Optimal Model Averaging Estimation for the Varying-Coefficient Partially Linear Models with Missing Responses" . | MATHEMATICS 11 . 8 (2023) . |
| APA | Zeng, Jie , Cheng, Weihu , Hu, Guozhi . Optimal Model Averaging Estimation for the Varying-Coefficient Partially Linear Models with Missing Responses . | MATHEMATICS , 2023 , 11 (8) . |
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Abstract ：
Tolerance intervals (TIs) are commonly employed in numerous industries, ranging from engineering to pharmaceuticals. However, closed-form TIs are unavailable for most distributions. Although some approximate methods can be used to obtain TIs, coverage probabilities (CPs) of these TIs cannot achieve the nominal level, or can be even far different from the nominal level. In this study, we propose two content-adjusted procedures for TIs based on bootstrap. The first one is based on the bootstrap sample quantile, while the second one is based on the asymptotic normality of empirical distribution. The simulation results show that the two calibration procedures can improve CPs of TIs for some non-normal distributions according to extensive numerical simulations, and they are both proved to be effective through real data examples.
Keyword ：
non-normal distributions non-normal distributions content correction content correction tolerance intervals tolerance intervals bootstrap calibration bootstrap calibration calibration interval calibration interval
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| GB/T 7714 | Jiao, Junjun , Zhao, Xu , Cheng, Weihu . Content-adjusted tolerance intervals via bootstrap calibration [J]. | STAT , 2022 , 11 (1) . |
| MLA | Jiao, Junjun 等. "Content-adjusted tolerance intervals via bootstrap calibration" . | STAT 11 . 1 (2022) . |
| APA | Jiao, Junjun , Zhao, Xu , Cheng, Weihu . Content-adjusted tolerance intervals via bootstrap calibration . | STAT , 2022 , 11 (1) . |
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Abstract ：
Air pollution is a major global problem, closely related to economic and social development and ecological environment construction. Air pollution data for most regions of China have a close correlation with time and seasons and are affected by multidimensional factors such as meteorology and air quality. In contrast with classical peaks-over-threshold modeling approaches, we use a deep learning technique and three new dynamic conditional generalized Pareto distribution (DCP) models with weather and air quality factors for fitting the time-dependence of the air pollutant concentration and make statistical inferences about their application in air quality analysis. Specifically, in the proposed three DCP models, a dynamic autoregressive exponential function mechanism is applied for the time-varying scale parameter and tail index of the conditional generalized Pareto distribution, and a sufficiently high threshold is chosen using two threshold selection procedures. The probabilistic properties of the DCP model and the statistical properties of the maximum likelihood estimation (MLE) are investigated, simulating and showing the stability and sensitivity of the MLE estimations. The three proposed models are applied to fit the PM 2.5 time series in Beijing from 2015 to 2021. Real data are used to illustrate the advantages of the DCP, especially compared to the estimation volatility of GARCH and AIC or BIC criteria. The DCP model involving both the mixed weather and air quality factors performs better than the other two models with weather factors or air quality factors alone. Finally, a prediction model based on long short-term memory (LSTM) is used to predict PM 2.5 concentration, achieving ideal results.
Keyword ：
generalized Pareto distribution generalized Pareto distribution long short-term memory long short-term memory dynamic conditional autoregressive modeling dynamic conditional autoregressive modeling peaks over threshold peaks over threshold threshold selection threshold selection
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| GB/T 7714 | Huang, Chunli , Zhao, Xu , Cheng, Weihu et al. Statistical Inference of Dynamic Conditional Generalized Pareto Distribution with Weather and Air Quality Factors [J]. | MATHEMATICS , 2022 , 10 (9) . |
| MLA | Huang, Chunli et al. "Statistical Inference of Dynamic Conditional Generalized Pareto Distribution with Weather and Air Quality Factors" . | MATHEMATICS 10 . 9 (2022) . |
| APA | Huang, Chunli , Zhao, Xu , Cheng, Weihu , Ji, Qingqing , Duan, Qiao , Han, Yufei . Statistical Inference of Dynamic Conditional Generalized Pareto Distribution with Weather and Air Quality Factors . | MATHEMATICS , 2022 , 10 (9) . |
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Abstract ：
Growing interest in genomics research has called for new semiparametric models based on kernel machine regression for modeling health outcomes. Models containing redundant predictors often show unsatisfactory prediction performance. Thus, our task is to construct a method which can guarantee the estimation accuracy by removing redundant variables. Specifically, in this paper, based on the regularization method and an innovative class of garrotized kernel functions, we propose a novel penalized kernel machine method for a semiparametric logistic model. Our method can promise us high prediction accuracies, due to its capability of flexibly describing the complicated relationship between responses and predictors and its compatibility of the interactions among the predictors. In addition, our method can also remove the redundant variables. Our numerical experiments demonstrate that our method yields higher prediction accuracies compared to competing approaches.
Keyword ：
kernel machine kernel machine variable selection variable selection logistic model logistic model semiparametric model semiparametric model
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| GB/T 7714 | Zheng, Xia , Rong, Yaohua , Liu, Ling et al. A More Accurate Estimation of Semiparametric Logistic Regression [J]. | MATHEMATICS , 2021 , 9 (19) . |
| MLA | Zheng, Xia et al. "A More Accurate Estimation of Semiparametric Logistic Regression" . | MATHEMATICS 9 . 19 (2021) . |
| APA | Zheng, Xia , Rong, Yaohua , Liu, Ling , Cheng, Weihu . A More Accurate Estimation of Semiparametric Logistic Regression . | MATHEMATICS , 2021 , 9 (19) . |
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Abstract ：
In this paper, a new generalized t (new Gt) distribution based on a distribution construction approach is proposed and proved to be suitable for fitting both the data with high kurtosis and heavy tail. The main innovation of this article consists of four parts. First of all, the main characteristics and properties of this new distribution are outined. Secondly, we derive the explicit expression for the moments of order statistics as well as its corresponding variance-covariance matrix. Thirdly, we focus on the parameter estimation of this new Gt distribution and introduce several estimation methods, such as a modified method of moments (MMOM), a maximum likelihood estimation (MLE) using the EM algorithm, a novel iterative algorithm to acquire MLE, and improved probability weighted moments (IPWM). Through simulation studies, it can be concluded that the IPWM estimation performs better than the MLE using the EM algorithm and the MMOM in general. The newly-proposed iterative algorithm has better performance than the EM algorithm when the sample kurtosis is greater than 2.7. For four parameters of the new Gt distribution, a profile maximum likelihood approach using the EM algorithm is developed to deal with the estimation problem and obtain acceptable.
Keyword ：
improved PWM improved PWM order statistics order statistics parameter estimation parameter estimation generalized t distribution generalized t distribution EM algorithm EM algorithm
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| GB/T 7714 | Guan, Ruijie , Zhao, Xu , Cheng, Weihu et al. A New Generalized t Distribution Based on a Distribution Construction Method [J]. | MATHEMATICS , 2021 , 9 (19) . |
| MLA | Guan, Ruijie et al. "A New Generalized t Distribution Based on a Distribution Construction Method" . | MATHEMATICS 9 . 19 (2021) . |
| APA | Guan, Ruijie , Zhao, Xu , Cheng, Weihu , Rong, Yaohua . A New Generalized t Distribution Based on a Distribution Construction Method . | MATHEMATICS , 2021 , 9 (19) . |
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Abstract ：
在氢能源的开发和利用中,储氢设备的质量分级评价十分重要.本文利用最优加权法对改进的层次分析法的权重进行优化,得到了各因素的层次分析法—熵权法权重;参照承压容器的质量分级通则,构建高压储氢模拟容器进行质量分级模型.利用分级通则模型和我们所建立的模型对102个模拟储氢罐分别进行质量分级,发现两种分级的结果没有显著差异,但我们所建立的模型简便实用.
Keyword ：
熵权法 熵权法 统计建模 统计建模 储氢设备 储氢设备 质量分级 质量分级 层次分析法 层次分析法
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| GB/T 7714 | 徐奇 , 程维虎 , 段志祥 et al. 高压储氢设备质量分级评价统计建模研究 [J]. | 数理统计与管理 , 2021 , 40 (3) : 395-404 . |
| MLA | 徐奇 et al. "高压储氢设备质量分级评价统计建模研究" . | 数理统计与管理 40 . 3 (2021) : 395-404 . |
| APA | 徐奇 , 程维虎 , 段志祥 , 石坤 . 高压储氢设备质量分级评价统计建模研究 . | 数理统计与管理 , 2021 , 40 (3) , 395-404 . |
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Abstract ：
随机总体分位数的统计推断理论与方法一直是统计学研究的重要课题.其主要原因是分位数的应用涉及众多领域,且在各领域的研究中起到举足轻重的作用.本文系统地论述了基于样本次序统计量的总体分位数的非参数统计推断的理论和方法;给出了基于样本次序统计量的总体分位数的估计方法,总体两个分位数之差的置信区间,总体容许区间的求解方法及符号检验.希望有助于读者的科研与应用.
Keyword ：
容许区间 容许区间 置信区间 置信区间 总体分位数 总体分位数 次序统计量 次序统计量 非参数推断 非参数推断
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| GB/T 7714 | 赵旭 , 程维虎 . 基于样本次序统计量的总体分位数的非参数统计推断 [J]. | 应用数学学报 , 2021 , 44 (04) : 475-491 . |
| MLA | 赵旭 et al. "基于样本次序统计量的总体分位数的非参数统计推断" . | 应用数学学报 44 . 04 (2021) : 475-491 . |
| APA | 赵旭 , 程维虎 . 基于样本次序统计量的总体分位数的非参数统计推断 . | 应用数学学报 , 2021 , 44 (04) , 475-491 . |
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Abstract ：
In this paper, we propose a least-squares estimator based on Logistic transformation of order statistics (LLSE) and grouped LLSE for the generalized Logistic distribution. Some asymptotic results are provided. Two simulations are undertaken to assess the performance of the proposed method and to compare them with other methods suggested in this paper. The simulation results indicate that LLSE performs better than some other methods and grouped LLSE performs fairly well in small sample size. Finally, LLSE is applied to a real dataset.
Keyword ：
logistic transformation logistic transformation least squares least squares Generalized logistic distribution Generalized logistic distribution
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| GB/T 7714 | Chen, Haiqing , Zhao, Xu , Zhu, Leilei et al. Fitting generalized logistic distribution by least squares based on the logistic transformation of order statistics [J]. | COMMUNICATIONS IN STATISTICS-THEORY AND METHODS , 2021 , 52 (2) : 263-272 . |
| MLA | Chen, Haiqing et al. "Fitting generalized logistic distribution by least squares based on the logistic transformation of order statistics" . | COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 52 . 2 (2021) : 263-272 . |
| APA | Chen, Haiqing , Zhao, Xu , Zhu, Leilei , Cheng, Weihu , Xu, Lu . Fitting generalized logistic distribution by least squares based on the logistic transformation of order statistics . | COMMUNICATIONS IN STATISTICS-THEORY AND METHODS , 2021 , 52 (2) , 263-272 . |
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