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A comparative analysis of several multivariate zero-inflated and zero-modified models with applications in insurance

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2025年第7期54卷 2130-2157页

作者： Zhang, Pengcheng Pitt, David Wu, Xueyuan Shandong Univ Finance & Econ Sch Insurance Jinan Peoples R China Univ Melbourne Ctr Actuarial Studies Dept Econ Melbourne Vic Australia

Given that insurance companies often operate across multiple lines of insurance business, where claim frequencies on different lines are often correlated, it often becomes advantageous to employ multivariate count modeling where dependence between lines of business can be included in the modeling. Due to the operation of bonus-malus systems where there is a reward to the insurance policyholder for not claiming, claims data in automobile insurance often exhibits an excess of common zeros, a characteristic known as multivariate zero-inflation. In this article, we propose two approaches to address this feature. The first approach involves utilizing a multivariate zero-inflated model, where we artificially enhance the probability of common zeros based on standard multivariate count distributions. The second approach applies a multivariate zero-modified model, which separately handles the common zeros and the number of claims incurred in each line given that at least one claim occurs. We present several models under these frameworks, along with detailed inference procedures. In the applications section, we conduct a comprehensive comparative analysis of these models using data from an automobile insurance portfolio.

关键词： Multivariate zero-inflated model multivariate zero-modified model expectation-maximization algorithm minorization-maximization algorithm automobile insurance ratemaking

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Modeling intra-individual inter-trial EEG response variability in autism

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STATISTICS IN MEDICINE 2024年第17期43卷 3239-3263页

作者： Dong, Mingfei Telesca, Donatello Guindani, Michele Sugar, Catherine Webb, Sara J. Jeste, Shafali Dickinson, Abigail Levin, April R. Shic, Frederick Naples, Adam Faja, Susan Dawson, Geraldine Mcpartland, James C. Sentuerk, Damla Univ Calif Los Angeles Dept Biostat Los Angeles CA 90095 USA Univ Calif Los Angeles Dept Psychiat & Biobehav Sci Los Angeles CA USA Seattle Childrens Res Inst Ctr Child Hlth Behav & Dev Seattle WA USA Univ Washington Sch Med Dept Psychiat & Behav Sci Seattle WA USA Childrens Hosp Los Angeles Dept Pediat Div Neurol Los Angeles CA USA Boston Childrens Hosp Div Neurol Boston MA USA Harvard Med Sch Div Neurol Boston MA USA Univ Washington Sch Med Dept Pediat Seattle WA USA Yale Univ Sch Med Ctr Child Study New Haven CT USA Boston Childrens Hosp Div Dev Med Lab Cognit Neurosci Boston MA USA Harvard Med Sch Dept Pediat Boston MA USA Duke Univ Duke Ctr Autism & Brain Dev Durham NC USA

Autism spectrum disorder (autism) is a prevalent neurodevelopmental condition characterized by early emerging impairments in social behavior and communication. EEG represents a powerful and non-invasive tool for examining functional brain differences in autism. Recent EEG evidence suggests that greater intra-individual trial-to-trial variability across EEG responses in stimulus-related tasks may characterize brain differences in autism. Traditional analysis of EEG data largely focuses on mean trends of the trial-averaged data, where trial-level analysis is rarely performed due to low neural signal to noise ratio. We propose to use nonlinear (shape-invariant) mixed effects (NLME) models to study intra-individual inter-trial EEG response variability using trial-level EEG data. By providing more precise metrics of response variability, this approach could enrich our understanding of neural disparities in autism and potentially aid the identification of objective markers. The proposed multilevel NLME models quantify variability in the signal's interpretable and widely recognized features (e.g., latency and amplitude) while also regularizing estimation based on noisy trial-level data. Even though NLME models have been studied for more than three decades, existing methods cannot scale up to large data sets. We propose computationally feasible estimation and inference methods via the use of a novel minorization-maximization (MM) algorithm. Extensive simulations are conducted to show the efficacy of the proposed procedures. Applications to data from a large national consortium find that children with autism have larger intra-individual inter-trial variability in P1 latency in a visual evoked potential (VEP) task, compared to their neurotypical peers.

关键词： autism spectrum disorder (autism) electroencephalography intra-individual inter-trial variability minorization-maximization algorithm nonlinear mixed effects models

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Efficient algorithms for survival data with multiple outcomes using the frailty model

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STATISTICAL METHODS IN MEDICAL RESEARCH 2023年第1期32卷 118-132页

作者： Huang, Xifen Xu, Jinfeng Zhou, Yunpeng Yunnan Normal Univ Sch Math Kunming Yunnan Peoples R China City Univ Hong Kong Dept Biostat Hong Kong Peoples R China Univ Hong Kong Dept Stat & Actuarial Sci Hong Kong Peoples R China

Survival data with multiple outcomes are frequently encountered in biomedical investigations. An illustrative example comes from Alzheimer's Disease Neuroimaging Initiative study where the cognitively normal subjects may clinically progress to mild cognitive impairment and/or Alzheimer's disease dementia. Transition time from normal cognition to mild cognitive impairment and that from mild cognitive impairment to Alzheimer's disease are expected to be correlated within subjects and the dependence is often accommodated by the frailty (random effects). Estimation in the frailty model unavoidably involves multiple integrations which may be intractable and hence leads to severe computational challenges, especially in the presence of high-dimensional covariates. In this paper, we propose efficient minorization-maximization algorithms in the frailty model for survival data with multiple outcomes. The alternating direction method of multipliers is further incorporated for simultaneous variable selection and homogeneity pursuit via regularization and fusion. Extensive simulation studies are conducted to assess the performance of the proposed algorithms. An application to the Alzheimer's Disease Neuroimaging Initiative data is also provided to illustrate their practical utilities.

关键词： Alternating direction method of multipliers Alzheimer's Disease Neuroimaging Initiative homogeneity pursuit minorization-maximization algorithm sparsity the frailty model

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Robust variable selection for the varying index coefficient models

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JOURNAL OF THE KOREAN STATISTICAL SOCIETY 2023年第4期52卷 767-793页

作者： Zou, Hang Jiang, Yunlu Jinan Univ Coll Econ Dept Stat & Data Sci Guangzhou 510632 Peoples R China

Recently, the statistical inference of the varying index coefficient model has been widely concerned. However, to the best of our knowledge, there has no existing robust variable selection method for the varying index coefficient model in the presence of outliers in the response and covariates. To overcome this difficulty, we develop a robust variable selection method for the varying index coefficient model via the exponential squared loss (ESL) function in this article. We first approximate nonparametric functions by B-spline basis functions and then apply the minorization-maximization (MM) algorithm and the Fisher scoring algorithm to calculate the proposed estimators. Under some mild conditions, the theoretical properties of the proposed estimators are established. Furthermore, we propose a data-driven procedure to select the tuning parameters. Some numerical simulations are conducted to illustrate the finite sample performance of the proposed method. Finally, the analysis of New Zealand workforce data reveals the merit of the proposed method.

关键词： Varying index coefficient model Exponential squared loss function Robust variable selection minorization-maximization algorithm

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Joint Resource Management for Intelligent Reflecting Surface-Aided Visible Light Communications

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2022年第8期21卷 6508-6522页

作者： Sun, Shiyuan Yang, Fang Song, Jian Han, Zhu Tsinghua Univ Beijing Natl Res Ctr Informat Sci & Technol Dept Elect Engn Beijing 100084 Peoples R China Tsinghua Univ Shenzhen Res Inst Key Lab Digital TV Syst Guangdong Prov & Shenzhen Shenzhen 518057 Peoples R China Univ Houston Dept Elect & Comp Engn Houston TX 77004 USA Kyung Hee Univ Dept Comp Sci & Engn Seoul 446701 South Korea

Though visible light communication (VLC) is a significant supplement to current communication technologies, disadvantages such as the sensitivity to obstacles limit its development and commercialization. As a revolutionizing technology, intelligent reflecting surface (IRS) offers an ability to reconfigure the wireless environment dynamically and passively, which is considered beneficial to improve the performance of VLC. This paper devotes to investigating the effect of VLC IRS and putting forward a joint resource management method for an instantaneous IRS-aided VLC system. To this end, the line-of-sight (LoS) and non-LoS channel gains are first discussed under the point source assumption, after which the system model is established and the optimization problem is formulated. Then, the frozen variable algorithm and minorization-maximization algorithm are proposed to iteratively maximize the overall spectral efficiency (SE), and detailed discussions on the weak/severe interference cases and computational complexity analysis are carried out. Moreover, numerical results are provided to show the improvement of SE and the effects of the proposed algorithms, which offers beneficial insights on joint resource management of IRS-aided VLC.

关键词： Visible light communication Light emitting diodes Wireless communication Resource management Optical transmitters Radio frequency Optimization Visible light communication (VLC) intelligent reflecting surface (IRS) spectral efficiency maximization joint resource management frozen variable algorithm minorization-maximization algorithm

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Generalized case-cohort and inference for Cox's model with parameter constraints

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2022年第7期51卷 3487-3512页

作者： Pan, Yingli Deng, Lifeng Hubei Univ Fac Math & Stat Hubei Key Lab Appl Math Wuhan Peoples R China Shandong Univ Sci & Technol Coll Math & Syst Sci Qingdao 266590 Shandong Peoples R China

To reduce the cost and improve the efficiency of studies, the generalized case-cohort design, in which the risk-factors include the subcohort members sampled by simple random sample from the full cohort, augmented with another subset sampled from the failure of interest outside the subcohort, has been widely used in many prevention trials and epidemiological cohort studies. In modeling process, including prior information about the parameters into consideration can further improve the study efficiency. In this article, regression analysis of Cox's model with parameter constraints under the generalized case-cohort design is studied. A working likelihood function is constructed for the estimation of the model parameters. The asymptotic properties of the constrained estimation are derived by using the Karush-Kuhn-Tucker conditions. A constrained minorization-maximization algorithm is developed for the calculation of the constrained estimator. Simulation studies are conducted to evaluate the finite-sample performance of our proposed estimator. We demonstrate the practicability of the proposed approach with a data set from a Wilms tumor study.

关键词： Cox's model ConStrained estimation Generalized case-cohort design Karush-Kuhn-Tucker conditions minorization-maximization algorithm

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Estimating the class prior for positive and unlabelled data via logistic regression

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ADVANCES IN DATA ANALYSIS AND CLASSIFICATION 2021年第4期15卷 1039-1068页

作者： Lazecka, Malgorzata Mielniczuk, Jan Teisseyre, Pawel Polish Acad Sci Inst Comp Sci Warsaw Poland Warsaw Univ Technol Fac Math & Informat Sci Warsaw Poland

In the paper, we revisit the problem of class prior probability estimation with positive and unlabelled data gathered in a single-sample scenario. The task is important as it is known that in positive unlabelled setting, a classifier can be successfully learned if the class prior is available. We show that without additional assumptions, class prior probability is not identifiable and thus the existing non-parametric estimators are necessarily biased in general if extra assumptions are not imposed. The magnitude of their bias is also investigated. The problem becomes identifiable when the probabilistic structure satisfies mild semi-parametric assumptions. Consequently, we propose a method based on a logistic fit and a concave minorization of its (non-concave) log-likelihood. The experiments conducted on artificial and benchmark datasets as well as on a large clinical database MIMIC indicate that the estimation errors for the proposed method are usually lower than for its competitors and that it is robust against departures from logistic settings.

关键词： Positive unlabelled learning Class prior estimation Logistic regression Non-convex optimisation minorization-maximization algorithm

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Penalized generalized estimating equations approach to longitudinal data with multinomial responses

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JOURNAL OF THE KOREAN STATISTICAL SOCIETY 2021年第3期50卷 844-859页

作者： Kamruzzaman, Md Kwon, Oran Park, Taesung Seoul Natl Univ Dept Stat Seoul 08826 South Korea Ewha Womans Univ Dept Nutr Sci & Food Management Seoul 120750 South Korea Seoul Natl Univ Interdisciplinary Program Bioinformat Seoul 08826 South Korea

In high-dimensional longitudinal data with multinomial response, the number of covariates is always much larger than the number of subjects and when modelling such data, variable selection is always an important issue. In this study, we developed the penalized generalized estimating equation for multinomial responses for identifying important variables and estimation of their regression coefficients simultaneously. An iterative algorithm is used to solve the penalized estimating equation by combining the Fisher-scoring algorithm and minorization-maximization algorithm. We used a penalty term to regularize the slope part only because category-specific intercept terms should be included in the multinomial model. We conducted a simulation study to investigate the performance of the proposed method and demonstrated its performance using real dataset.

关键词： High-dimensional data Longitudinal data Multinomial response minorization-maximization algorithm Smoothly Clipped Absolute Deviation penalty Minimax Concave Penalty Variable selection

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Mean regression model for the zero-truncated Poisson distribution and its generalization

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2023年 179卷

作者： Li, Xun-Jian Sun, Yuan Tian, Guo-Liang Liang, Jiajuan Shi, Jianhua Southern Univ Sci & Technol Dept Stat & Data Sci Shenzhen 518055 Guangdong Peoples R China HKBU United Int Coll Dept Stat & Data Sci Guangdong Prov Key Lab Interdisciplinary Res & App BNU Zhuhai 519087 Guangdong Peoples R China Minnan Normal Univ Sch Math & Stat Zhangzhou 363000 Fujian Peoples R China

Zero-truncated count data (e.g., days of staying in hospital;survival weeks of female patients with breast cancer) often arise in various fields such as medical studies. To model such data, the zero-truncated Poisson (ZTP) distribution is commonly utilized to investigate the relationship between the response counts and a set of covariates. For existing ZTP regression models, it is very hard to explain the regression coefficients beta or it is quite difficult to perform a constrained optimization to calculate the maximum likelihood estimates (MLEs) of beta. This paper aims to introduce a new mean regression model for the ZTP distribution with a clear interpretation about the regression coefficients. Because of challenge that the original Poisson mean parameter lambda i cannot be expressed explicitly the ZTP mean parameter mu i, an embedded Newton-Raphson algorithm is developed calculate the MLEs of regression coefficients. The construction of bootstrap confidence intervals is presented and three hypothesis tests (i.e., the likelihood ratio test, the Wald test and the score test) are considered. Furthermore, the ZTP mean regression model is generalized to the mean regression model for the k-truncated Poisson distribution. Simulation studies are conducted and two real data are analyzed to illustrate the proposed model and methods.(c) 2022 Elsevier B.V. All rights reserved.

关键词： Embedded Newton-Raphson algorithm k-truncated Poisson Mean regression minorization-maximization algorithm Zero-truncated Poisson

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A quadratic upper bound algorithm for regression analysis of credit risk under the proportional hazards model with case-cohort data

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STATISTICS AND COMPUTING 2023年第4期33卷 78-78页

作者： Huang, Chen Ding, Jieli Feng, Yanqin Wuhan Univ Sch Math & Stat Wuhan 430072 Hubei Peoples R China

A case-cohort design is a cost-effective biased-sampling scheme in studies on survival data. We study the regression analysis of credit risk by fitting the proportional hazards model to data collected via the case-cohort design. Using the minorization-maximization principle, we develop a new quadratic upper-bound algorithm for the calculation of estimators and obtain the convergence of the algorithm. The proposed algorithm involves the inversion of the derived upper-bound matrix only one time in the whole process and the upper-bound matrix is independent of parameters. These features make the proposed algorithm have simple update and low per-iterative cost, especially to large-dimensional problems. Rcpp is an R package which enables users to write R extensions with C++. In this paper, we write the program of the proposed algorithm via Rcpp and improve the efficiency of R program execution and realize the fast computing. We conduct simulation studies to illustrate the performance of the proposed algorithm. We analyze a real data example from a mortgage dataset for evaluating credit risk.

关键词： Case-cohort design minorization-maximization algorithm Quadratic upper bound The proportional hazards model

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