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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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Maximum likelihood estimation of Gaussian mixture models without matrix operations

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ADVANCES IN DATA ANALYSIS AND CLASSIFICATION 2015年第4期9卷 371-394页

作者： Nguyen, Hien D. McLachlan, Geoffrey J. Univ Queensland Dept Math Sch Math & Phys Brisbane Qld 4072 Australia

The Gaussian mixture model (GMM) is a popular tool for multivariate analysis, in particular, cluster analysis. The expectation-maximization (EM) algorithm is generally used to perform maximum likelihood (ML) estimation for GMMs due to the M-step existing in closed form and its desirable numerical properties, such as monotonicity. However, the EM algorithm has been criticized as being slow to converge and thus computationally expensive in some situations. In this article, we introduce the linear regression characterization (LRC) of the GMM. We show that the parameters of an LRC of the GMM can be mapped back to the natural parameters, and that a minorization-maximization (MM) algorithm can be constructed, which retains the desirable numerical properties of the EM algorithm, without the use of matrix operations. We prove that the ML estimators of the LRC parameters are consistent and asymptotically normal, like their natural counterparts. Furthermore, we show that the LRC allows for simple handling of singularities in the ML estimation of GMMs. Using numerical simulations in the R programming environment, we then demonstrate that the MM algorithm can be faster than the EM algorithm in various large data situations, where sample sizes range in the tens to hundreds of thousands and for estimating models with up to 16 mixture components on multivariate data with up to 16 variables.

关键词： Gaussian mixture model minorization-maximization algorithm matrix operation-free Linear Regression

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Statistical inference for generalized case-cohort design under the proportional hazards model with parameter constraints

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2019年第8期48卷 2467-2486页

作者： Pan, Yingli Ding, Jieli Liu, Yanyan Huazhong Univ Sci & Technol Sch Math & Stat Wuhan Hubei Peoples R China Wuhan Univ Sch Math & Stat Wuhan 430072 Hubei Peoples R China

The generalized case-cohort design is widely used in large cohort studies to reduce the cost and improve the efficiency. Taking prior information of parameters into consideration in modeling process can further raise the inference efficiency. In this paper, we consider fitting proportional hazards model with constraints for generalized case-cohort studies. We establish a working likelihood function for the estimation of model parameters. The asymptotic properties of the proposed estimator are derived via the Karush-Kuhn-Tucker conditions, and their finite properties are assessed by simulation studies. A modified minorization-maximization algorithm is developed for the numerical calculation of the constrained estimator. An application to a Wilms tumor study demonstrates the utility of the proposed method in practice.

关键词： Constrained estimation Generalized case-cohort design Karush-Kuhn-Tucker conditions minorization-maximization algorithm Proportional hazards model

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Laplace mixture of linear experts

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2016年 93卷 177-191页

作者： Nguyen, Hien D. McLachlan, Geoffrey J. Univ Queensland Sch Math & Phys St Lucia Qld 4072 Australia

Mixture of Linear Experts (MoLE) models provide a popular framework for modeling nonlinear regression data. The majority of applications of MoLE models utilizes a Gaussian distribution for regression error. Such assumptions are known to be sensitive to outliers. The use of a Laplace distributed error is investigated. This model is named the Laplace MoLE (LMoLE). Links are drawn between the Laplace error model and the least absolute deviations regression criterion, which is known to be robust among a wide class of criteria. Through application of the minorization maximization algorithm framework, an algorithm is derived that monotonically increases the likelihood in the estimation of the LMoLE model parameters. It is proven that the maximum likelihood estimator (MLE) for the parameter vector of the LMoLE is consistent. Through simulation studies, the robustness of the LMoLE model over the Gaussian MOLE model is demonstrated, and support for the consistency of the MLE is provided. An application of the LMoLE model to the analysis of a climate science data set is described. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Laplace distribution minorization-maximization algorithm Mixture of experts Robust regression

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Mixture of Time-Dependent Growth Models with an Application to Blue Swimmer Crab Length-Frequency Data

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BIOMETRICS 2016年第4期72卷 1255-1265页

作者： Lloyd-Jones, Luke R. Nguyen, Hien D. McLachlan, Geoffrey J. Sumpton, Wayne Wang, You-Gan Univ Queensland Queensland Brain Inst Ctr Neurogenet & Stat Genom Brisbane Qld 4072 Australia Univ Queensland Sch Math & Phys Brisbane Qld 4072 Australia Ecosci Precinct Queensland Dept Agr & Fisheries Joe Baker StDutton Pk Brisbane Qld 4102 Australia Queensland Univ Technol Sch Math Sci Brisbane Qld 4000 Australia

Understanding how aquatic species grow is fundamental in fisheries because stock assessment often relies on growth dependent statistical models. Length-frequency-based methods become important when more applicable data for growth model estimation are either not available or very expensive. In this article, we develop a new framework for growth estimation from length-frequency data using a generalized von Bertalanffy growth model (VBGM) framework that allows for time-dependent covariates to be incorporated. A finite mixture of normal distributions is used to model the length-frequency cohorts of each month with the means constrained to follow a VBGM. The variances of the finite mixture components are constrained to be a function of mean length, reducing the number of parameters and allowing for an estimate of the variance at any length. To optimize the likelihood, we use a minorization-maximization (MM) algorithm with a Nelder-Mead sub-step. This work was motivated by the decline in catches of the blue swimmer crab (BSC) (Portunus armatus) off the east coast of Queensland, Australia. We test the method with a simulation study and then apply it to the BSC fishery data.

关键词： Blue swimmer crab Growth model estimation Length-frequency data minorization-maximization algorithm Mixture modeling

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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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A novel MM algorithm and the mode-sharing method in Bayesian computation for the analysis of general incomplete categorical data

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2019年 140卷 122-143页

作者： Tian, Guo-Liang Liu, Yin Tang, Man-Lai Li, Tao Southern Univ Sci & Technol Dept Math Shenzhen 518055 Guangdong Peoples R China Zhongnan Univ Econ & Law Sch Math & Stat Wuhan 430073 Hubei Peoples R China Hang Seng Univ Hong Kong Sch Decis Sci Dept Math & Stat Siu Lek YuenShatin Hong Kong Peoples R China

Incomplete categorical data often occur in the fields such as biomedicine, epidemiology, psychology, sports and so on. In this paper, we first introduce a novel minorization-maximization (MM) algorithm to calculate the maximum likelihood estimates (MLEs) of parameters and the posterior modes for the analysis of general incomplete categorical data. Although the data augmentation (DA) algorithm and Gibbs sampling as the corresponding stochastic counterparts of the expectation-maximization (EM) and ECM algorithms are developed very well, up to now, little work has been done on creating stochastic versions to the existing MM algorithms. This is the first paper to propose a mode-sharing method in Bayesian computation for general incomplete categorical data by developing a new acceptance-rejection (AR) algorithm aided with the proposed MM algorithm. The key idea is to construct a class of envelope densities indexed by a working parameter and to identify a specific envelope density which can overcome the four drawbacks associated with the traditional AR algorithm. The proposed mode-sharing based AR algorithm has three significant characteristics: (I) it can automatically establish a family of envelope densities {g(lambda)(.): lambda is an element of S-lambda} indexed by a working parameter lambda, where each member in the family shares mode with the posterior density;(II) with the onedimensional grid method searching over the finite interval S-lambda,S- it can identify an optimal working parameter lambda(opt) by maximizing the theoretical acceptance probability, yielding a best easy-sampling envelope density g lambda(opt) (.), which is more dispersive than the posterior density;(III) it can obtain the optimal envelope constant c(opt) by using the mode-sharing theorem (indicating that the high-dimensional optimization can be completely avoided) or by using the proposed MM algorithm again. Finally, a toy model and three real data sets are used to illustrate the proposed meth

关键词： Acceptance-rejection algorithm Bayesian analysis General incomplete categorical data minorization-maximization algorithm Mode-sharing method

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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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Regression analysis for the proportional hazards model with parameter constraints under case-cohort design

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2018年 117卷 194-206页

作者： Deng, Lifeng Ding, Jieli Liu, Yanyan Wei, Chengdong Huazhong Univ Sci & Technol Sch Math & Stat Wuhan 430074 Hubei Peoples R China Wuhan Univ Sch Math & Stat Wuhan 430072 Hubei Peoples R China Guangxi Teachers Educ Univ Sch Math & Stat Nanning 530023 Guangxi Peoples R China

To reduce the cost and improve the efficiency of cohort studies, case-cohort design is a widely used biased-sampling scheme for time-to-event data. In modeling process, case cohort studies can benefit further from taking parameters' prior information, such as the histological type and disease stage of the cancer in medical, the liquidity and market demand of the enterprise in finance. Regression analysis of the proportional hazards model with parameter constraints under case-cohort design is studied. Asymptotic properties are derived by applying the Lagrangian method based on Karush-Kuhn-Tucker conditions. The consistency and asymptotic normality of the constrained estimator are established. A modified minorization-maximization algorithm is developed for the calculation of the constrained estimator. Simulation studies are conducted to assess the finite-sample performance of the proposed method. An application to a Wilms tumor study demonstrates the utility of the proposed method in practice. (C) 2017 Published by Elsevier B.V.

关键词： Case-cohort design Proportional hazards model Constrained estimation Karush-Kuhn-Tucker conditions 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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