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学者姓名：程维虎
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Abstract ：
In this paper, we introduce a family of distributions known as generalized scale mixtures of asymmetric generalized normal distributions (GSMAGN), characterized by remarkable flexibility in shape. We propose a novel finite mixture model based on this distribution family, offering an effective tool for modeling intricate data featuring skewness, heavy tails, and multi-modality. To facilitate parameter estimation for this model, we devise an ECM-PLA ensemble algorithm that combines the Profile Likelihood Approach (PLA) with the classical Expectation Conditional Maximization (ECM) algorithm. By incorporating analytical expressions in the E-step and manageable computations in the M-step, this approach significantly enhances computational speed and overall efficiency. Furthermore, we persent the closed-form expressions for the observed information matrix, which serves as an approximation for the asymptotic covariance matrix of the maximum likelihood estimates. Additionally, we expound upon the corresponding consistency characteristics inherent to this particular mixture model. The applicability of the proposed model is elucidated through several simulation studies and practical datasets.
Keyword ：
Generalized scale mixtures Generalized scale mixtures Finite mixture model Finite mixture model EM-type algorithm EM-type algorithm Model based clustering Model based clustering Asymmetric generalized normal distribution Asymmetric generalized normal distribution
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| GB/T 7714 | Guan, Ruijie , Jiao, Junjun , Cheng, Weihu et al. A novel finite mixture model based on the generalized scale mixtures of asymmetric generalized normal distributions: properties, estimation methodology and applications [J]. | COMPUTATIONAL STATISTICS , 2024 . |
| MLA | Guan, Ruijie et al. "A novel finite mixture model based on the generalized scale mixtures of asymmetric generalized normal distributions: properties, estimation methodology and applications" . | COMPUTATIONAL STATISTICS (2024) . |
| APA | Guan, Ruijie , Jiao, Junjun , Cheng, Weihu , Hu, Guozhi . A novel finite mixture model based on the generalized scale mixtures of asymmetric generalized normal distributions: properties, estimation methodology and applications . | COMPUTATIONAL STATISTICS , 2024 . |
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Abstract ：
In recent years, some interested data can be recorded only if the values fall within an interval range, and the responses are often subject to censoring. Attempting to perform effective statistical analysis with censored, especially heavy-tailed and asymmetric data, can be difficult. In this paper, we develop a novel linear regression model based on the proposed skewed generalized t distribution for censored data. The likelihood-based inference and diagnostic analysis are established using the Expectation/Conditional Maximization Either algorithm in conjunction with smoothing approximate functions. We derive relevant measures to perform global influence for this novel model and develop local influence analysis based on the conditional expectation of the complete-data log-likelihood function. Some useful perturbation schemes are discussed. We illustrate the finite sample performance and the robustness of the proposed method by simulation studies. The proposed model is compared with other procedures based on a real dataset, and a sensitivity analysis is also conducted.
Keyword ：
EM-type algorithms EM-type algorithms residual analysis residual analysis influence analysis influence analysis skewed generalized t distribution skewed generalized t distribution Censored regression model Censored regression model
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| GB/T 7714 | Lian, Chengdi , Rong, Yaohua , Liang, Jinwen et al. Inference and diagnostics for censored linear regression model with skewed generalized t distribution [J]. | JOURNAL OF APPLIED STATISTICS , 2024 . |
| MLA | Lian, Chengdi et al. "Inference and diagnostics for censored linear regression model with skewed generalized t distribution" . | JOURNAL OF APPLIED STATISTICS (2024) . |
| APA | Lian, Chengdi , Rong, Yaohua , Liang, Jinwen , Guan, Ruijie , Cheng, Weihu . Inference and diagnostics for censored linear regression model with skewed generalized t distribution . | JOURNAL OF APPLIED STATISTICS , 2024 . |
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Abstract ：
Intuitionistic fuzzy sets provide a viable framework for modelling lifetime distribution characteristics, particularly in scenarios with measurement imprecision. This is accomplished by utilizing membership and non-membership degrees to accurately express the complexities of data uncertainty. Nonetheless, the complexities of some cases necessitate a more advanced approach of imprecise data, motivating the use of generalized intuitionistic fuzzy sets (GenIFSs). The use of GenIFSs represents a flexible modeling strategy that is characterized by the careful incorporation of an extra level of hesitancy, which effectively clarifies the underlying ambiguity and uncertainty present in reliability evaluations. The study employs a methodology based on generalized intuitionistic fuzzy distributions to thoroughly examine the uncertainty related to the parameters and reliability characteristics present in the Burr XII distribution. The goal is to provide a more accurate evaluation of reliability measurements by addressing the inherent ambiguity in the distribution's shape parameter. Various reliability measurements, such as reliability, hazard rate, and conditional reliability functions, are derived for the Burr XII distribution. This extensive analysis is carried out within the context of the generalized intuitionistic fuzzy sets paradigm, improving the understanding of the Burr XII distribution's reliability measurements and providing important insights into its performance for the study of various types of systems. To facilitate understanding and point to practical application, the findings are shown graphically and contrasted across various cut-set values using a valuable numerical example.
Keyword ：
alpha,beta-cut sets alpha,beta-cut sets generalized intuitionistic fuzzy probability (GenIFP) generalized intuitionistic fuzzy probability (GenIFP) new type generalized intuitionistic fuzzy set (GenIFS) new type generalized intuitionistic fuzzy set (GenIFS) generalized intuitionistic fuzzy reliability characteristics (GenIFRCs) generalized intuitionistic fuzzy reliability characteristics (GenIFRCs) Burr XII distribution Burr XII distribution
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| GB/T 7714 | Kalam, Abdul , Cheng, Weihu , Stefanatos, Dionisis et al. Statistical Reliability Assessment with Generalized Intuitionistic Fuzzy Burr XII Distribution [J]. | PROCESSES , 2024 , 12 (5) . |
| MLA | Kalam, Abdul et al. "Statistical Reliability Assessment with Generalized Intuitionistic Fuzzy Burr XII Distribution" . | PROCESSES 12 . 5 (2024) . |
| APA | Kalam, Abdul , Cheng, Weihu , Stefanatos, Dionisis , Shah, Sayed Kifayat . Statistical Reliability Assessment with Generalized Intuitionistic Fuzzy Burr XII Distribution . | PROCESSES , 2024 , 12 (5) . |
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Abstract ：
Generalized Pareto distribution (GPD), an asymmetrical distribution, primarily models exceedances over a high threshold in many applications. Within the peaks-over-threshold (POT) framework, we consider a new GPD parameter estimation method to estimate a common tail risk measure, the value at risk (VaR). The proposed method is more suitable for the POT framework and makes full use of data information. Specifically, our estimation method builds upon the generalized probability weighted moments method and integrates it with the nonlinear weighted least squares method. We use exceedances for the GPD, minimizing the sum of squared differences between the sample and population moments of a function of GPD random variables. At the same time, the proposed estimator uses three iterations and assigns weight to further improving the estimated performance. Under Monte Carlo simulations and with a real heavy-tailed dataset, the simulation results show the advantage of the newly proposed estimator, particularly when VaRs are at high confidence levels. In addition, by simulating other heavy-tailed distributions, our method still exhibits good performance in estimating misjudgment distributions.
Keyword ：
extreme value theory extreme value theory extreme quantile estimation extreme quantile estimation parameter estimation parameter estimation generalized Pareto distribution generalized Pareto distribution
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| GB/T 7714 | Chen, Wenru , Zhao, Xu , Zhou, Mi et al. Statistical Inference and Application of Asymmetrical Generalized Pareto Distribution Based on Peaks-Over-Threshold Model [J]. | SYMMETRY-BASEL , 2024 , 16 (3) . |
| MLA | Chen, Wenru et al. "Statistical Inference and Application of Asymmetrical Generalized Pareto Distribution Based on Peaks-Over-Threshold Model" . | SYMMETRY-BASEL 16 . 3 (2024) . |
| APA | Chen, Wenru , Zhao, Xu , Zhou, Mi , Chen, Haiqing , Ji, Qingqing , Cheng, Weihu . Statistical Inference and Application of Asymmetrical Generalized Pareto Distribution Based on Peaks-Over-Threshold Model . | SYMMETRY-BASEL , 2024 , 16 (3) . |
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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 et al. "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 et al. "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 ：
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 et al. "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 ：
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 et al. "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 ：
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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