异方差的线性混合模型的参数估计

本文研究既含有固定效应又含有随机效应的线性混合模型,在随机效应的方差不同即异方差情况下,即考虑方差受外界因素的影响,如温度、湿度等,我们称之为协变量,在有协变量情况下对方差建立对数线性模型,运用最大似然估计讨论了固定效应的估计和随机效应的预测,并且用约束最大似然(REML)方法研究对数线性模型中参数和随机误差中参数(离差参数)的估计,并讨论估计量的性质及离差参数估计量的渐近正态性。     

一类有条件异方差的非线性自回归模型的高阶矩

本文对一类非线性时间序列模型ｘｔ＝φ（ｘｔ－１，…，ｘｔ－ｐ）＋εｔｈ（ｘｔ－１，…，ｘｔ－ｐ）给出了高阶矩的存在条件。     

含方程误差的异方差重复测量误差模型参数估计

对于含测量误差的重复测量数据,协变量与响应变量真值之间可能不存在完全匹配关系,即存在方程误差.且变量真值的测量误差方差可能与样本的某种特征有关,即存在异方差性.以此类数据为驱动,讨论了含方程误差的异方差重复测量误差模型的建模和估计问题,基于EM算法给出了模型参数的显式极大似然迭代估计.最后通过模拟计算和实例分析,讨论了模型和估计方法的有效性.     

多维广义自回归条件异方差模型

In this paper,by making use of the Hadamard product of matrices,a natural and reasonable generalization of the univariate GARCH(Generalized Autoregressive Conditional heteroscedastic)process introduced by Bollerslev(J.Econometrics 31(1986),307-327)to the multivariate case is proposed.The conditions for the existence of strictly stationary and ergodic solutions and the existence of higher order moments for this class of parametric models are derived.     

非对称广义自回归条件异方差的新模型

本文提出了一个新的非对称广义自回归条件异方差的新模型,证明了该模型宽平稳及其最简模型偶数价矩存在的充要条件。     

非线性随机效应模型的异方差性检验

随机效应模型广泛应用于刻画重复测量数据的特征．在该模型中,随机误差的方差包括受试群体内部及受试群体之间两项方差．Ｚｈａｎｇ和 Ｗｅｉｓｓ ２０００年研究了线性随机效应模型的异方差检验,本文对非线性随机效应模型,分别讨论了群体内、群体间和多变量的异方差性的检验问题,得到了检验的ｓｃｏｒｅ统计量,并讨论了三种情形下,相应的ｓｃｏｒｅ函数之间的关系．最后给出一个数值例子说明上述方法的有用性．     

门限自回归模型条件异方差的Kolmogorov-Smirnov检验

门限自回归模型被广泛地用于许多领域，当建立或使用这类模型时，一个重要问题是需要知道是否存在条件异方差。在本文中，我们对这个问题提出一个非参数检验，检验的大样本理论被给出，我们还通过数值模拟研究了检验方法的有限样本性质。结果表示检验有好的功效。经验百分位点还被给出。     

中国证券市场股指波动的条件异方差特性分析

股指的波动具有持续性、集聚性 ,如何进行判别 ?本文用 Garch模型理论探讨沪深股指的这种条件异方差特征 ,进一步分析波动是否影响股指未来变化 ,以及股市对利好、利空的消息是否存在不对称的反映。同时 ,比较不同类型的股指的共性及差异 ,并对上述现象作了解释和说明。     

基于异方差的自回归预测模型的参数估计及其应用

从齐性方差的线性回归模型参数估计的最小二乘法出发,通过对统计资料的适当变换,利用加权最小二乘法,获得了异方差的线性自回归模型和四种异方差的非线性自回归模型的参数估计公式,并举例阐述了估计公式的应用.     

随机权函数非线性回归模型的异方差统计分析

在回归分析中，随机误差是否存在方差齐性是理论与实际工作者都十分关心的问题，方差齐性假设并不总是正确的，在线性和非线性回归中关于异方差的诊断问题已有许多讨论（[1],[2],[4],[5]）。本文在韦博成（1995）讨论了加权非线性回归模型的基础上，用随机系数的方法，讨论随机权函数非线性回归模型中的异方差检验问题，得到了方差齐性检验的似然比统计量和score统计量，同时，当模型存在异方差时，本文给出了估计方差的一种方法。     

多层线性模型参数估计的MCEM算法

应用Monte Carlo EM(MCEM)算法给出了多层线性模型参数估计的新方法,解决了EM算法用于模型时积分计算困难的问题,并通过数值模拟将方法的估计结果与EM算法的进行比较,验证了方法的有效性和可行性.     

Bayesian Hierarchical Space–time Modeling of Earthquake Data

Stochastic earthquake models are often based on a marked point process approach as for instance presented in Vere-Jones (Int. J. Forecast., 11:503–538, 1995). This gives a fine resolution both in space and time making it possible to represent each earthquake. However, it is not obvious that this approach is advantageous when aiming at earthquake predictions. In the present paper we take a coarse point of view considering grid cells of 0.5 × 0.5°, or about 50 × 50 km, and time periods of 4 months, which seems suitable for predictions. More specifically, we will discuss different alternatives of a Bayesian hierarchical space–time model in the spirit of Wikle et al. (Environ. Ecol. Stat., 5:117–154, 1998). For each time period the observations are the magnitudes of the largest observed earthquake within each grid cell. As data we apply parts of an earthquake catalogue provided by The Northern California Earthquake Data Center where we limit ourselves to the area 32–37° N, 115–120° W for the time period January 1981 through December 1999 containing the Landers and Hector Mine earthquakes of magnitudes, respectively, 7.3 and 7.1 on the Richter scale. Based on space-time model alternatives one step earthquake predictions for the time periods containing these two events for all grid cells are arrived at. The model alternatives are implemented within an MCMC framework in Matlab. The model alternative that gives the overall best predictions based on a standard loss is claimed to give new knowledge on the spatial and time related dependencies between earthquakes. Also considering a specially designed loss using spatially averages of the 90th percentiles of the predicted values distribution of each cell it is clear that the best model predicts the high risk areas rather well. By using these percentiles we believe that one has a valuable tool for defining high and low risk areas in a region in short term predictions.      

Bayesian Semiparametric Density Deconvolution in the Presence of Conditionally Heteroscedastic Measurement Errors

We consider the problem of estimating the density of a random variable when precise measurements on the variable are not available, but replicated proxies contaminated with measurement error are available for sufficiently many subjects. Under the assumption of additive measurement errors this reduces to a problem of deconvolution of densities. Deconvolution methods often make restrictive and unrealistic assumptions about the density of interest and the distribution of measurement errors, for example, normality and homoscedasticity and thus independence from the variable of interest. This article relaxes these assumptions and introduces novel Bayesian semiparametric methodology based on Dirichlet process mixture models for robust deconvolution of densities in the presence of conditionally heteroscedastic measurement errors. In particular, the models can adapt to asymmetry, heavy tails, and multimodality. In simulation experiments, we show that our methods vastly outperform a recent Bayesian approach based on estimating the densities via mixtures of splines. We apply our methods to data from nutritional epidemiology. Even in the special case when the measurement errors are homoscedastic, our methodology is novel and dominates other methods that have been proposed previously. Additional simulation results, instructions on getting access to the dataset and R programs implementing our methods are included as part of online supplementary materials.     

Hierarchical linear regression models for conditional quantiles

The quantile regression has several useful features and therefore is gradually developing into a comprehensive approach to the statistical analysis of linear and nonlinear response models, but it cannot deal effectively with the data with a hierarchical structure. In practice, the existence of such data hierarchies is neither accidental nor ignorable, it is a common phenomenon. To ignore this hierarchical data structure risks overlooking the importance of group effects, and may also render many of the traditional statistical analysis techniques used for studying data relationships invalid. On the other hand, the hierarchical models take a hierarchical data structure into account and have also many applications in statistics, ranging from overdispersion to constructing min-max estimators. However, the hierarchical models are virtually the mean regression, therefore, they cannot be used to characterize the entire conditional distribution of a dependent variable given high-dimensional covariates. Furthermore, the estimated coefficient vector (marginal effects) is sensitive to an outlier observation on the dependent variable. In this article, a new approach, which is based on the Gauss-Seidel iteration and taking a full advantage of the quantile regression and hierarchical models, is developed. On the theoretical front, we also consider the asymptotic properties of the new method, obtaining the simple conditions for an n1/2-convergence and an asymptotic normality. We also illustrate the use of the technique with the real educational data which is hierarchical and how the results can be explained.     

Heteroscedastic nonlinear regression models based on scale mixtures of skew-normal distributions

An extension of some standard likelihood based procedures to heteroscedastic nonlinear regression models under scale mixtures of skew-normal (SMSN) distributions is developed. We derive a simple EM-type algorithm for iteratively computing maximum likelihood (ML) estimates and the observed information matrix is derived analytically. Simulation studies demonstrate the robustness of this flexible class against outlying and influential observations, as well as nice asymptotic properties of the proposed EM-type ML estimates. Finally, the methodology is illustrated using an ultrasonic calibration data.     

无失效数据失效率的综合多层Bayes估计

文章对指数分布无失效数据的失效率,在先验分布为Ｇａｍｍａ分布时,在引进失效信息后,给出了多层Ｂａｙｅｓ估计以及综合多层Ｂａｙｅｓ估计,并给出了可靠度的综合估计。最后,结合实际问题进行了计算     

无失效数据的Bayes和多层Bayes估计

对无失效数据的研究 ,是近些年来遇到的一个新问题 ,在实际问题中迫切需要解决 ,这项工作具有理论和实际应用价值 .本文对无失效数据 (ti,ni) ,在时刻ti 的失效概率pi=p{T 相似文献   

二项分布无失效数据可靠度的多层Bayes估计

文章对二次分布无失效数据的可靠度,在先验分布为Ｂｅｔａ分布时,给出了可靠度的多层Ｂａｙｅｓ估计。最后,结合实际问题进行了计算。     

分层广义线性模型在准备金评估中的建模研究

考虑到赔付流量三角形数据同一事故年反复观测的纵向特征以及数据结构的层次性,建立了分层广义线性模型.与通常的随机模型相比,分层广义线性模型不但可以选择条件反应变量的分布而且风险参数分布范围也更加广泛.利用h-似然函数估计分层广义线性模型的模型参数,降低了计算量.为使模型具有可比性,评估模型的预测精度,推导了模型预测误差的估计式.为充分利用已知赔付信息,将赔付额和赔付次数两种赔付信息纳入未决赔款准备金评估模型,建立了两阶段分层广义线性模型.在线性预测量中考虑了各种固定效应和随机效应以及模型结构的散布参数,改进了线性预估量结构.研究表明:分层广义线性模型对于数据的各种分布及形式都具有很好的适应性,更加符合保险实务现实的赔付规律.     

基于GP/GA的数据建模方法

传统的数据建模方法 ,需要利用统计学和人工智能技术对数据进行探索性分析 ,操作者必须掌握大量的先验知识。将遗传程序设计 (GP)和遗传算法 (GA)应用到数据建模中 ,实现模型的自动获取。试验结果表明 ,在遗传操作中执行子树变异操作 ,将性能好的模型结构引入到进化中 ,可以提高遗传程序设计的收敛速度