Estimating Frailty Models via Poisson Hierarchical Generalized Linear Models

Frailty models extend proportional hazards models to multivariate survival data. Hierarchical-likelihood provides a simple unified framework for various random effect models such as hierarchical generalized linear models, frailty models, and mixed linear models with censoring. Wereview the hierarchical-likelihood estimation methods for frailty models. Hierarchical-likelihood for frailty models can be expressed as that for Poisson hierarchical generalized linear models. Frailty models can thus be fitted using Poisson hierarchical generalized linear models. Properties of the new methodology are demonstrated by simulation. The new method reduces the bias of maximum likelihood and penalized likelihood estimates.     

Consistency and asymptotic normality of the maximum quasi-likelihood estimator in quasi-likelihood nonlinear models with random regressors

This paper proposes some regularity conditions, which result in the existence, strong consistency and asymptotic normality of maximum quasi-likelihood estimator （MQLE） in quasi-likelihood nonlinear models （QLNM） with random regressors. The asymptotic results of generalized linear models （GLM） with random regressors are generalized to QLNM with random regressors.     

相依误差广义线性模型的M估计的Bahadur表示

考虑如下广义线性模型y_i=h(x~T_i,β)+e_i=1,2,…,n,其中e_i=G(…,ε_(i-1),ε_i),h是一个连续可导函数,ε_i是独立同分布的随机变量,并且它的期望为0,方差σ~2有限.本文给出了参数β的M估计,并且得到了该估计的Bahadur表示,该结论推广了线性模型的相关结论.应用M估计的Bahadur表示,得到了相依误差的线性回归模型,poisson模型,logistic模型和独立误差的广义线性模型等模型的渐近性质.     

Local asymptotic normality of multivariate ARMA processes with a linear trend

The local asymptotic normality (LAN) property is established for multivariate ARMA models with a linear trend or, equivalently, for multivariate general linear models with ARMA error term. In contrast with earlier univariate results, the central sequence here is correlogram-based, i.e. expressed in terms of a generalized concept of residual cross-covariance function.     

非线性再生散度随机效应模型的贝叶斯分析

非线性再生散度随机效应模型是一类非常广泛的统计模型，包括了线性随机效应模型、非线性随机效应模型、广义线性随机效应模型和指数族非线性随机效应模型等．本文研究非线性再生散度随机效应模型的贝叶斯分析．通过视随机效应为缺失数据以及应用结合Gibbs抽样技术和Metropolis-Hastings算法（简称MH算法）的混合算法获得了模型参数与随机效应的同时贝叶斯估计．最后，用一个模拟研究和一个实际例子说明上述算法的可行眭．     

Prediction and calibration in generalized linear models

This paper concerns prediction and calibration in generalized linear models. A new predictive procedure, giving improved prediction intervals, is briefly reviewed and further theoretical results, useful for calculations, are presented. Indeed, the calibration problem is faced within the classical approach and a suitable solution is obtained by inverting the associated improved prediction procedure. This calibration technique gives accurate confidence regions and it constitutes a substantial improvement over both the estimative solution and the naive solution, which involves, even for non-linear and non-normal models, the results available for the linear Gaussian case. Finally, some useful explicit formulae for the construction of prediction and calibration intervals are presented, with regard to generalized linear models with alternative error terms and link functions. This research was partially supported by a grant from Ministero dell’Instruzione, dell’Università e della Ricerca, Italy.     

非寿险分类费率模型的比较研究和实证分析

非寿险分类费率的厘定通常采用的方法有单项分析法、最小偏差法和广义线性模型,特别是后面两种方法在非寿险实务中应用十分广泛,精算文献中对这两种方法的理论和应用研究也较多,但对二者的比较研究较少。本文首先对最小偏差模型和广义线性模型进行了简要介绍,之后对这两种分类费率模型进行了系统的比较研究,总结了它们各自的优缺点以及二者之间的一些等价关系,最后通过一组实际的汽车保险数据讨论了它们的应用。     

Exponentiated generalized linear exponential distribution

A new generalization of the linear exponential distribution is recently proposed by Mahmoud and Alam [1], called as the generalized linear exponential distribution. Another generalization of the linear exponential was introduced by Sarhan and Kundu  and , named as the generalized linear failure rate distribution. This paper proposes a more generalization of the linear exponential distribution which generalizes the two. We refer to this new generalization as the exponentiated generalized linear exponential distribution. The new distribution is important since it contains as special sub-models some widely well known distributions in addition to the above two models, such as the exponentiated Weibull distribution among many others. It also provides more flexibility to analyze complex real data sets. We study some statistical properties for the new distribution. We discuss maximum likelihood estimation of the distribution parameters. Three real data sets are analyzed using the new distribution, which show that the exponentiated generalized linear exponential distribution can be used quite effectively in analyzing real lifetime data.     

约束条件下线性模型协方差阵扰动的影响分析

该文研究了协方差阵扰动和数据删除对最佳线性无偏估计(BLUE)的影响问题, 给出了在约束条件下一般线性模型与在约束条件下Gauss-Markov模型及在约束条件下数据删除模型中回归参数β的BLUE之间的关系式. 作者还定义了度量影响大小的广义Cook距离D_V并给出了D_V的两个计算公式.     

A Note on the Optimality of Generalized Cross-validation Bandwidth Selection in Partially Linear Models with Kernel Smoothing Estimator

The issue of selection of bandwidth in kernel smoothing method is considered within the context of partially linear models, hi this paper, we study the asymptotic behavior of the bandwidth choice based on generalized cross-validation （CCV） approach and prove that this bandwidth choice is asymptotically optimal. Numerical simulation are also conducted to investigate the empirical performance of generalized cross-valldation.     

广义线性模型在汽车保险定价的应用

对非寿险产品分类费率的厘定通常采用单项分析法、最小偏差法和多元线性回归等方法。虽然这些方法在非寿险产品定价中仍然占有一度之地,但由于保险数据的特殊性,它们的缺陷越来越受到人们的重视。本文简要分析了这些传统定价方法存在的缺陷,介绍了非寿险精算中典型的广义线性模型,并通过汽车第三者责任保险的损失数据说明了广义线性模型在非寿险产品定价中的具体应用,以及应用广义线性模型时应该注意的几个问题。     

线性混合模型中方差分量的广义推断

本文考虑了线性混合模型中方差分量的假设检验和区间估计问题.基于广义P-值和广义置信区间的概念,构造了对应于随机效应的单个方差分量的精确检验和置信区间.所构造的广义p-值和广义置信区间是最小充分统计量的函数.对于两个独立线性混合模型中对应于随机效应的方差分量的比较,建立了精确检验和置信区间.进-步,研究了所给检验和置信区间的统计性质,给出了这些检验方法与文献中已有方法的功效比较的模拟结果.模拟结果表明,新检验在功效方面有显著的改进.最后,通过-个实例来演示本文方怯.     

Sampling Schemes for Bayesian Variable Selection in Generalized Linear Models

Bayesian approaches to prediction and the assessment of predictive uncertainty in generalized linear models are often based on averaging predictions over different models, and this requires methods for accounting for model uncertainty. When there are linear dependencies among potential predictor variables in a generalized linear model, existing Markov chain Monte Carlo algorithms for sampling from the posterior distribution on the model and parameter space in Bayesian variable selection problems may not work well. This article describes a sampling algorithm based on the Swendsen-Wang algorithm for the Ising model, and which works well when the predictors are far from orthogonality. In problems of variable selection for generalized linear models we can index different models by a binary parameter vector, where each binary variable indicates whether or not a given predictor variable is included in the model. The posterior distribution on the model is a distribution on this collection of binary strings, and by thinking of this posterior distribution as a binary spatial field we apply a sampling scheme inspired by the Swendsen-Wang algorithm for the Ising model in order to sample from the model posterior distribution. The algorithm we describe extends a similar algorithm for variable selection problems in linear models. The benefits of the algorithm are demonstrated for both real and simulated data.     

Anisotropic Cosmology with a Dilaton Field Coupled to Ghost Dark Energy

We study a dilaton scalar field coupled to ghost dark energy in an anisotropic universe. The evolution of dark energy, which dominates the universe, can be completely described by a single dilaton scalar field. This connection allows reconstructing the kinetic energy and also the dynamics of the dilaton scalar field according to the evolution of the energy density. Using the latest observational data, we obtain bounds on the ghost dark energy models and also on generalized dark matter and dark energy. For this, we investigate how the expansion history H(z) is determined by observational quantities. We calculate the evolution of density perturbations in the linear regime for both ghost and generalized ghost dark energy and compare the results with ΛCDM models. We discuss the justification of the generalized second law of thermodynamics in a Bianchi type-I universe. The obtained model is stable for large time intervals but is unstable at small times.     

A note on the identifiability of nonparametric and semiparametric mixtures of GLMs

In this article, we first propose a semiparametric mixture of generalized linear models (GLMs) and a nonparametric mixture of GLMs, and then establish identifiability results under mild conditions.     

偏t分布假设下的空间效应模型及其应用

在非寿险索赔强度预测中,目前使用最为广泛的是广义线性模型。索赔强度的广义线性模型假设因变量服从伽马分布或逆高斯分布,且在预测项中仅能考虑协变量的线性效应。这些限制性条件都有可能影响索赔强度预测结果的准确性。本文对索赔强度的广义线性模型进行了推广:用偏T分布代替常用的伽马分布和逆高斯分布;在预测项中引入惩罚样条函数来描述连续型协变量的非线性效应;考虑索赔强度在不同地区的差异性和相邻地区的相依性。最后基于一组实际的车损险数据进行了实证研究,结果表明,本文的推广模型可以明显提高索赔强度预测模型的拟合优度。     

Robust sure independence screening for ultrahigh dimensional non-normal data

Sure independence screening（SIS） has been proposed to reduce the ultrahigh dimensionality down to a moderate scale and proved to enjoy the sure screening property under Gaussian linear models.However,the observed response is often skewed or heavy-tailed with extreme values in practice,which may dramatically deteriorate the performance of SIS.To this end,we propose a new robust sure independence screening（RoSIS） via considering the correlation between each predictor and the distribution function of the response.The proposed approach contributes to the literature in the following three folds： First,it is able to reduce ultrahigh dimensionality effectively.Second,it is robust to heavy tails or extreme values in the response.Third,it possesses both sure screening property and ranking consistency property under milder conditions.Furthermore,we demonstrate its excellent finite sample performance through numerical simulations and a real data example.     

Estimation of Lyapunov spectrum and model selection for a chaotic time series

The estimation of the Lyapunov spectrum for a chaotic time series is discussed in this study. Three models: the local linear (LL) model; the local polynomial (LP) model and the global radial basis function (RBF) model, are compared for estimating the Lyapunov spectrum in this study. The number of neighbors for training the LL model and the LP model; the number of centers for building the RBF model, have been determined by the generalized degree of freedom for a chaotic time series. The above models have been applied to three artificial chaotic time series and two real-world time series, the numerical results show that the model-chosen LL model provides more accurate estimation than other models for clean data set while the RBF model behaves more robust to noise than other models for noisy data set.     

GLMMLasso: An Algorithm for High-Dimensional Generalized Linear Mixed Models Using ℓ1-Penalization

We propose an ?₁-penalized algorithm for fitting high-dimensional generalized linear mixed models (GLMMs). GLMMs can be viewed as an extension of generalized linear models for clustered observations. Our Lasso-type approach for GLMMs should be mainly used as variable screening method to reduce the number of variables below the sample size. We then suggest a refitting by maximum likelihood based on the selected variables only. This is an effective correction to overcome problems stemming from the variable screening procedure that are more severe with GLMMs than for generalized linear models. We illustrate the performance of our algorithm on simulated as well as on real data examples. Supplementary materials are available online and the algorithm is implemented in the R package glmmixedlasso.