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Parameter estimation of the WMTD model

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Applied Mathematics(A Journal of Chinese Universities) 2009年第4期24卷 379-388页

作者： LUO Ji QIU Hong-bing School of Mathematics and Statistics Zhejiang University of Finance and Economics Hangzhou 310018 China School of Finance and Statistics East China Normal University Shanghai 200241 China Department of Applied Mathematics Guangdong University of Technology Guangzhou 510006 China

The MTD （mixture transition distribution） model based on Weibull distribution （WMTD model） is proposed in this paper, which is aimed at its parameter estimation. An em algorithm for estimation is given and shown to work well by some simulations. And bootstrap method is used to obtain confidence regions for the parameters. Finally, the results of a real example--predicting stock prices--show that the WMTD model proposed is able to capture the features of the data from thick-tailed distribution better than GMTD （mixture transition distribution） model.

关键词： Markov chain em algorithm Weibull distribution bootstrap confidence region

A skew–normal mixture of joint location, scale and skewness models

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Applied Mathematics(A Journal of Chinese Universities) 2016年第3期31卷 283-295页

作者： LI Hui-qiong WU Liu-cang YI Jie-yi Department of statistics Yunnan University Faculty of Science Kunming University of Science and Technology School of Mathematical Sciences Beijing Normal University

Normal mixture regression models are one of the most important statistical data analysis tools in a heterogeneous population. When the data set under consideration involves asymmetric outcomes, in the last two decades, the skew normal distribution has been shown beneficial in dealing with asymmetric data in various theoretic and applied problems. In this paper, we propose and study a novel class of models： a skew-normal mixture of joint location, scale and skewness models to analyze the heteroscedastic skew-normal data coming from a heterogeneous population. The issues of maximum likelihood estimation are addressed. In particular, an Expectation-Maximization （em） algorithm for estimating the model parameters is developed. Properties of the estimators of the regression coefficients are evaluated through Monte Carlo experiments. Results from the analysis of a real data set from the Body Mass Index （BMI） data are presented.

关键词： mixture regression models mixture of joint location scale and skewness models em algorithm maximum likelihood estimation skew-normal mixtures

Joint Modeling of Failure Time Data with Transformation Model and Longitudinal Data When Covariates are Measured with Errors

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Acta Mathematicae Applicatae Sinica 2012年第4期28卷 663-672页

作者： Xi-ming CHENG Qi GONG School of Applied Science Beijing Information Science and Technology University Academy of Mathematics and Systems Science Chinese Academy of Sciences Department of Statistics University of Missouri

Semiparametric transformation models provide a class of flexible models for regression analysis of failure time data. Several authors have discussed them under different situations when covariates are time- independent （Chen et al., 2002; Cheng et al., 1995; Fine et al., 1998）. In this paper, we consider fitting these models to right-censored data when covariates are time-dependent longitudinal variables and, furthermore, may suffer measurement errors. For estimation, we investigate the maximum likelihood approach, and an em algorithm is developed. Simulation results show that the proposed method is appropriate for practical application, and an illustrative example is provided.

关键词： em algorithm linear random effects model maximum likelihood estimation measurement error

Modeling Reliability Engineering Data Using Scale-Invariant Quasi-Inverse Lindley Model

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Computers, Materials & Continua 2022年第7期72卷 1847-1860页

作者： Mohamed Kayid Tareq Alsayed Department of Statistics and Operations Research College of ScienceKing Saud UniversityRiyadhSaudi Arabia

An important property that any lifetime model should satisfy is scale *** this paper,a new scale-invariant quasi-inverse Lindley(QIL)model is presented and *** basic properties,including moments,quantiles,skewness,kurtosis,and Lorenz curve,have been *** addition,the well-known dynamic reliability measures,such as failure rate(FR),reversed failure rate(RFR),mean residual life(MRL),mean inactivity time(MIT),quantile residual life(QRL),and quantile inactivity time(QIT)are *** FR function considers the decreasing or upside-down bathtub-shaped,and the MRL and median residual lifetime may have a bathtub-shaped *** parameters of the model are estimated by applying the maximum likelihood method and the expectation-maximization(em)*** em algorithm is an iterative method suitable for models with a latent variable,for example,when we have mixture or competing risk models.A simulation study is then conducted to examine the consistency and efficiency of the estimators and compare *** simulation study shows that the em approach provides a better estimation of the ***,the proposed model is fitted to a reliability engineering data set along with some *** Akaike information criterion(AIC),Kolmogorov-Smirnov(K-S),Cramer-von Mises(CVM),and Anderson Darling(AD)statistics are used to compare the considered models.

关键词： Inverse Lindley distribution reliability measures maximum likelihood estimation em algorithm

Hazard Model with Random Treatment Time-Lag Effect

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Acta Mathematica Sinica,English Series 2023年第9期39卷 1755-1767页

作者： Xin Ye Yan Yan Liu School of Mathematics and Statistics Wuhan UniversityWuhan430072P.R.China

In clinical studies,it is often that the medical treatments take a period of time before having an effect on patients and the delayed time may vary from person to *** though there exists a rich literature developing methods to estimate the time-lag period and treatment effects after lag time,most of these existing studies assume a fixed lag *** this paper,we propose a hazard model incorporating a random treatment time-lag effect to describe the heterogeneous treatment effect among *** em algorithm is used to obtain the maximum likelihood *** give the asymptotic properties of the proposed estimator and evaluate its performance via simulation *** application of the proposed method to real data is provided.

关键词： Random lag time treatment effect right censored data em algorithm

Random change point model with an application to the China Household Finance Survey

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Science China Mathematics 2024年第10期67卷 2373-2386页

作者： Meng Li Lingxi Gao Guangming Lv Xingwei Tong School of Statistics Beijing Normal UniversityBeijing 100875China

We consider a linear model with a change point according to the unknown random threshold of a covariate. We give the expectation-maximization(em) estimations of the regression and change point parameters. The existence of the random change point is detected by the supremum(SUP) test of score statistics. Theoretically, we establish the convergence and asymptotic distribution of the estimation and show that the em estimates converge in distribution to a normal distribution. In addition, the numerical performance of the proposed approach is demonstrated through simulation studies. Finally, applying our methodology to household financial decisions, we see that the average debt tolerance of Chinese households is estimated to be 1.1364 times the sum of total household income and financial assets. The effect of assets and income on consumption shows a rapid decline if the household exceeds the average debt tolerance.

关键词： random change point em algorithm SUP test debt nancial vulnerability

Population Size Estimation with Covariate Values Missing Non-ignorable

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Acta Mathematicae Applicatae Sinica 2016年第3期32卷 659-668页

作者： Li-ping LIU Zhi-chao GUO Xiao-gang DUAN LMAM and CSS School of Mathematical Sciences Peking University Beijing 100871 China Beijing Normal University Beijing 100875 China

The main purpose of this paper is using capture-recapture data to estimate the population size when some covariate values are missing, possibly non-ignorable. Conditional likelihood method is adopted, with a sub-model describing various missing mechanisms. The derived estimate is proved to be asymptotically normal, and simulation studies via a version of em algorithm show that it is approximately unbiased. The proposed method is applied to a real example, and the result is compared with previous ones.

关键词： capture-recapture conditional likelihood em algorithm missing non-ignorable

Analysis of Two-sample Censored Data Using a Semiparametric Mixture Model

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Acta Mathematicae Applicatae Sinica 2009年第3期25卷 389-398页

作者： Gang Li Chien-tai Lin Department of Biostatistics University of California Los Angeles CA 90095 U.S.A. Department of Mathematics Tamkang University Tamsui 251 Taiwan

In this article we study a semiparametric mixture model for the two-sample problem with right censored data. The model implies that the densities for the continuous outcomes are related by a parametric tilt but otherwise unspecified. It provides a useful alternative to the Cox （1972） proportional hazards model for the comparison of treatments based on right censored survival data. We propose an iterative algorithm for the semiparametric maximum likelihood estimates of the parametric and nonparametric components of the model. The performance of the proposed method is studied using simulation. We illustrate our method in an application to melanoma.

关键词： Biased sampling em algorithm maximum likelihood estimation mixture model semiparametric model

Regression Analysis of Right-censored Failure Time Data with Missing Censoring Indicators

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Acta Mathematicae Applicatae Sinica 2009年第3期25卷 415-426页

作者： Ping Chen Ren He Jun-shan Shen Jian-guo Sun Department of Statistics University of Missouri 146 Middlebush Hall Columbia MO 65211 U.S.A. School of Mathematical Sciences Peking University Beijing 100871 China

This paper discusses regression analysis of right-censored failure time data when censoring indicators are missing for some subjects. Several methods have been developed for the analysis under different situations and especially, Goetghebeur and Ryan considered the situation where both the failure time and the censoring time follow the proportional hazards models marginally and developed an estimating equation approach. One limitation of their approach is that the two baseline hazard functions were assumed to be proportional to each other. We consider the same problem and present an efficient estimation procedure for regression parameters that does not require the proportionality assumption. An em algorithm is developed and the method is evaluated by a simulation study, which indicates that the proposed methodology performs well for practical situations. An illustrative example is provided.

关键词： Efficient estimation em algorithm incomplete data missing at random Proportional hazards model