Mixtures of semiparametric varying coefficient models for longitudinal data with nonignorable dropout

Informative dropout often arise in longitudinal data. In this paper we propose a mixture model in which the responses follow a semiparametric varying coefficient random effects model and some of the regression coefficients depend on the dropout time in a non-parametric way. The local linear version of the profile-kernel method is used to estimate the parameters of the model. The proposed estimators are shown to be consistent and asymptotically normal, and the finite performance of the estimators is evaluated by numerical simulation.     

Reducing component estimation for varying coefficient models with longitudinal data

Varying-coefficient models with longitudinal observations are very useful in epidemiology and some other practical fields.In this paper,a reducing component procedure is proposed for es- timating the unknown functions and their derivatives in very general models,in which the unknown coefficient functions admit different or the same degrees of smoothness and the covariates can be time- dependent.The asymptotic properties of the estimators,such as consistency,rate of convergence and asymptotic distribution,are derived.The asymptotic results show that the asymptotic variance of the reducing component estimators is smaller than that of the existing estimators when the coefficient functions admit different degrees of smoothness.Finite sample properties of our procedures are studied through Monte Carlo simulations.     

Influence diagnostics and outlier tests for varying coefficient mixed models

In this paper, we consider subset deletion diagnostics for fixed effects (coefficient functions), random effects and one variance component in varying coefficient mixed models (VCMMs). Some simple updated formulas are obtained, and based on which, Cook’s distance, joint influence and conditional influence are also investigated. Besides, since mean shift outlier models (MSOMs) are also efficient to detect outliers, we establish an equivalence between deletion models and MSOMs, which is not only suitable for fixed effects but also for random effects, and test statistics for outliers are then constructed. As a byproduct, we obtain the nonparametric “delete = replace” identity. Our influence diagnostics methods are illustrated through a simulated example and a real data set.     

Statistical estimation in varying coefficient models with surrogate data and validation sampling

Varying coefficient error-in-covariables models are considered with surrogate data and validation sampling. Without specifying any error structure equation, two estimators for the coefficient function vector are suggested by using the local linear kernel smoothing technique. The proposed estimators are proved to be asymptotically normal. A bootstrap procedure is suggested to estimate the asymptotic variances. The data-driven bandwidth selection method is discussed. A simulation study is conducted to evaluate the proposed estimating methods.     

Model detection and variable selection for varying coefficient models with longitudinal data

In this paper, we consider the problem of variable selection and model detection in varying coefficient models with longitudinal data. We propose a combined penalization procedure to select the significant variables, detect the true structure of the model and estimate the unknown regression coefficients simultaneously. With appropriate selection of the tuning parameters, we show that the proposed procedure is consistent in both variable selection and the separation of varying and constant coefficients, and the penalized estimators have the oracle property. Finite sample performances of the proposed method are illustrated by some simulation studies and the real data analysis.     

Joint modeling of failure time data with transformation model and longitudinal data when covariates are measured with errors

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 timeindependent (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.     

偏正态数据下众数回归模型的统计诊断

为了更好地拟合偏态数据,充分提取偏态数据的信息,针对偏正态数据建立了众数回归模型,并基于Pena距离统计量对众数回归模型进行统计断研究,得到了众数回归模型的Pena距离表达式以及高杠杆异常点的诊断方法.利用EM算法与梯度下降法给出了众数回归模型参数的极大似然估计,根据数据删除模型计算似然距离、Cook距离和Pena距离统计量,绘制诊断统计图.通过Monte Carlo模拟试验和实例分析比较,说明文章提出的方法行之有效,并在一定条件下Pena距离对异常点或强影响点的诊断优于似然距离和Cook距离.     

Binomial proportion estimation in longitudinal data with non-ignorable non-response

Non-random missing data poses serious problems in longitudinal studies. The binomial distribution parameter becomes to be unidentifiable without any other auxiliary information or assumption when it suffers from ignorable missing data. Existing methods are mostly based on the log-linear regression model. In this article, a model is proposed for longitudinal data with non-ignorable non-response. It is considered to use the pre-test baseline data to improve the identifiability of the post-test parameter. Furthermore, we derive the identified estimation (IE), the maximum likelihood estimation (MLE) and its associated variance for the post-test parameter. The simulation study based on the model of this paper shows that the proposed approach gives promising results.     

The joint distributions of several important actuarial diagnostics in the classical risk model

In this paper we examine the joint distributions of several actuarial diagnostics which are important to insurers’ running in the classical risk model. They include the time of the surplus process leaving zero ultimately (simply, the ultimately leaving-time), the number of zero, the surplus immediately prior to ruin, the deficit at ruin, the supreme and minimum profits before ruin, the supreme profits and deficit until it leaves zero ultimately and so on. We obtain explicit expressions for their joint distributions mainly by strong Markov property of the surplus process—a technique used by Wu et al. (2002) [J. Appl. Math., in press], which is completely different from former contributions on this topic. Further, we give the exact calculating results for them when the individual claim amounts are exponentially distributed.     

带有误差变量的自回归模型的局部多项式估计

该文主要研究带有误差变量的自回归模型的自回归函数的非参数估计问题,应用卷积核函数,给出了自回归函数的局部多项式估计,考察了局部多项式估计的相合性和渐近正态性,最后作了模拟计算.     

A hidden Markov model for informative dropout in longitudinal response data with crisis states

We adopt a hidden state approach for the analysis of longitudinal data subject to dropout. Motivated by two applied studies, we assume that subjects can move between three states: stable, crisis, dropout. Dropout is observed but the other two states are not. During a possibly transient crisis state both the longitudinal response distribution and the probability of dropout can differ from those for the stable state. We adopt a linear mixed effects model with subject-specific trajectories during stable periods and additional random jumps during crises. We place the model in the context of Rubin’s taxonomy and develop the associated likelihood. The methods are illustrated using the two motivating examples.     

Bayesian Influence Assessment in the Growth Curve Model with Unstructured Covariance

From a Bayesian point of view, in this paper we discuss the influence of a subset of observations on the posterior distributions of parameters in a growth curve model with unstructured covariance. The measure used to assess the influence is based on a Bayesian entropy, namely Kullback-Leibler divergence (KLD). Several new properties of the Bayesian entropy are studied, and analytically closed forms of the KLD measurement both for the matrix-variate normal distribution and the Wishart distribution are established. In the growth curve model, the KLD measurements for all combinations of the parameters are also studied. For illustration, a practical data set is analyzed using the proposed approach, which shows that the diagnostics measurements are useful in practice.     

具有一般协方差结构线性模型的局部影响评价

该文讨论了具有一般协方差结构线性模型的局部影响分析问题. 通过对广义Cook统计量中M/c的适当选取, 文章给出了一种对扰动的参数变换具有不变性质的局部影响度量. 在具协方差扰动模式下, 该文给出了回归系数和方差系数估计、最佳线性预测的局部影响诊断统计量.该结果与数据删除法进行了比较, 并通过实例进行了分析和说明.     

A mathematical model for the Multi-Levels Product Allocation Problem in a warehouse with compatibility constraints

The aim of this work is to address the products allocation problem in a multi-layers warehouse with compatibility constraints among the classes. The problem under study represents one of the most relevant topic in Logistics. The goal is to reduce, as much as possible, the delivery times; the inventories; the total logistic costs and to guarantee, at the same time, higher service levels (i.e., high customers satisfaction degree). In this work, a linear model to mathematically represent the problem is developed and its performance is evaluated on a set of instances, representing realistic situations. A sensitivity analysis is also carried out by considering the most relevant parameters of the model. Finally, an Iterated Local Search based heuristic is defined in order to solve large scale scenarios in a reasonable amount of time. Numerical results show that the proposed heuristic is able to find good quality solutions with a computational effort lower than that required to solve the proposed mathematical model.     

Stability and Hopf bifurcation in a predator–prey model with stage structure for the predator

A predator–prey system with stage structure for the predator and time delay due to the gestation of the predator is investigated. By analyzing the corresponding characteristic equations, the local stability of a positive equilibrium and two boundary equilibria of the system is discussed, respectively. Further, the existence of a Hopf bifurcation at the positive equilibrium is also studied. By using an iteration technique and comparison argument, respectively, sufficient conditions are derived for the global stability of the positive equilibrium and one of the boundary equilibria of the proposed system. As a result, the threshold is obtained for the permanence and extinction of the system. Numerical simulations are carried out to illustrate the main results.     

Nonparametric estimation of the purity of a quantum state in quantum homodyne tomography with noisy data

The aim of this paper is to answer an important issue in quantum mechanics, namely to estimate the purity of a quantum state of a light beam. Estimation of the purity is based on the results of quantum homodyne measurements performed on independent identically prepared quantum systems. The quantum state of the light is entirely characterized by the Wigner function, which can take negative values and must satisfy certain constraints of positivity imposed by quantum physics. We estimate the integrated squared Wigner function by a kernel-based second order U — statistic. This quadratic functional is a physical measure of the purity of the state. We also give an adaptive estimator, which does not depend on the smoothness parameters. We establish upper bounds of the minimax risk over a class of infinitely differentiable functions.      

Bayesian‐type count data models with varying coefficients: estimation and testing in the presence of overdispersion

In this paper we study varying‐coefficient models for count data. A Bayesian approach is taken to model the variability of the regression parameters. Based on a Kalman filter procedure the varying coefficients are estimated as the mode of the posterior distribution. All hyperparameters, including an overdispersion parameter in the negative binomial varying‐coefficient model (NBVC), are estimated as ML‐estimators using an EM‐type algorithm. A bootstrapping test of the fixed‐coefficient hypothesis against a varying‐coefficient alternative is proposed, which is evaluated running a simulation study. The study shows that the choice of a suitable count data model is of special importance in the framework of varying‐coefficient models. The methodology is illustrated analysing the determinants of the number of individual doctor visits. Copyright © 2001 John Wiley & Sons, Ltd.     

Stochastic stability and bifurcation for the chronic state in Marchuk’s model with noise

A stochastic differential equation modelling a Marchuk’s model is investigated. The stochasticity in the model is introduced by parameter perturbation which is a standard technique in stochastic population modelling. Firstly, the stochastic Marchuk’s model has been simplified by applying stochastic center manifold and stochastic average theory. Secondly, by using Lyapunov exponent and singular boundary theory, we analyze the local stochastic stability and global stochastic stability for stochastic Marchuk’s model, respectively. Thirdly, we explore the stochastic bifurcation of the stochastic Marchuk’s model according to invariant measure and stationary probability density. Some new criteria ensuring stochastic pitchfork bifurcation and P-bifurcation for stochastic Marchuk’s model are obtained, respectively.     

A rank estimator in the two-sample transformation model with randomly censored data

We consider the transformation model which is a generalization of Lehmann alternatives model. This model contains a parameter and a nonparametric part F ₁ which is a distribution function. We propose a kind of M-estimator of based on ranks in the presence of random censoring. It is nonparametric in the sense that we do not have to know F ₁. Moreover, it is simple and asymptotically normal. For the proportional hazards model with special censoring, we obtain the asymptotic relative efficiency of our estimator with respect to the best nonparametric estimator for this model. It is quite efficient for special values of . We also make a comparison between our estimator and other proposed estimators with real data.     

Remarks on between estimator in the intraclass correlation model with missing data

In this paper, we consider the between estimator under the intraclass correlation model with missing data. We give a necessary and sufficient condition for existing exact simultaneous confidence intervals for all contrasts in the means under the between transformed model, which indicates the F-test statistic and simultaneous confidence intervals, constructed by Seo et al. [T. Seo, J. Kikuchi, K. Koizumi, On simultaneous confidence intervals for all contracts in the means of the intraclass correlation model with missing data, J. Multivariate Anal. 97 (2006) 1976–1983] based on the between estimator, is invalid. Furthermore, using the distribution of the between estimator, we present the exact test statistics and confidence intervals for partial contrasts.