部分线性可加变量含误差模型的估计

作为可加模型和部分线性模型的推广,部分线性可加模型是一类应用广泛的半参数模型。文章主要讨论了当线性部分的协变量测量含误差时模型的估计问题,我们基于profile全最小二乘法构造了参数分量和模型误差方差的估计,并证明了估计量的渐近正态性。     

部分线性变系数模型的Backfitting约束估计

作为部分线性模型与变系数模型的推广,部分线性变系数模型是一类应用广泛的半参数模型.文章主要研究该模型线性部分存在约束条件下的估计和检验问题,首先基于backfitting方法给出了常数系数以及变系数部分的约束估计,其次构造了检验统计量用于检验约束条件.     

NA误差下线性模型最小绝对偏差估计的相合性

文章基于相依序列,研究了线性模型,在若干条件的假设下,建立了以NA序列为误差的线性模型未知参数的最小绝对偏差估计的渐近性质,如最小绝对偏差估计的强相合性.此结果是在较弱的条件下将文献[1]中独立误差情形下未知参数估计的相关结果推广到了NA误差下相应的结果.     

鞅差序列误差下线性模型的经验似然推断

文章在线性模型误差项为鞅差序列情形下,应用经验似然方法得到了关于回归系数β的对数经验似然比统计量渐近服从菇分布,从而得到了关于β的置信域。     

联合广义线性模型中的变量选择

在联合广义线性模型中,散度参数与均值都被赋予了广义线性模型的结构,本文主要考虑在只有分布的一阶矩和二阶矩指定的条件下,联合广义线性模型中均值部分的变量选择问题。本文采用广义拟似然函数,提出了新的模型选择准则(EAIC);该准则是Akaike信息准则的推广。论文通过模拟研究验证了该准则的效果。     

非寿险未决赔款准备金评估的两阶段广义线性混合模型

文章考虑了赔付额和赔付次数两种赔付信息,建立两阶段广义线性混合模型.为提高模型的适用范围,将赔付次数的分布假设由通常的泊松分布推广到过度分散泊松分布,将案均赔付额的分布假设由通常的伽玛分布拓宽到ED*类分布.通过对Hoerl曲线的改进来刻画赔付损失的进展模式,改善了模型的线性预估量.为了刻画不同模型的预测效果,给出了模型均方误差的理论推导和估计方法.以实际的保险数据为例,利用R软件进行实证分析.结果表明,建立的模型提高了未决赔款准备金评估的预测精度和适用范围.     

基于广义线性混合模型的经验费率厘定

信度模型是非寿险精算学中最为重要的成果.从20世纪初至今,信度理论先后经历了两个发展阶段:一是早期的有限波动信度模型;二是目前的最大精确信度模型.有限波动信度模型强调结果的稳定性,而最大精确信度模型强调结果的精确性.因此建立信度模型与广义线性混合模型之间的联系,通过对信度模型的分解可以看到:传统的信度理论对风险的刻画方法与广义线性混合模型的结构有极其相似的地方,故可以用广义线性混合模型来厘定经验费率.     

线性混合模型方差分量的谱分解估计

文章把文献[8]关于含有两个方差分量的线性混合效应模型的谱分解估计推广到一般线性混合效应模型,基本思想是通过把所研究的模型转化为含有两个方差分量的线性混合效应模型。首先研究如何构造含有三个方差分量的线性混合模型的谱分解估计,给出谱分解估计的无偏估计类。然后把所得到的结论推广到一般线性混合效应模型中。     

广义Gamma分布簇广义线性混合模型的构建

 本文在广义Gamma分布簇基础上引入异质性来构建广义线性混合模型。本文构建的广义Gamma分布簇广义线性混合模型在广义线性混合模型的框架下分析,通过参数重整技术把广义Gamma分布簇变量的建模问题与指数分布簇变量的建模问题联系起来,模型推断可以方便地利用广义线性混合模型和广义线性模型的研究成果,同时也可以方便地推广到其他模型。三参数广义Gamma分布可以收缩到两参数的Gamma分布、Weibull分布或指数分布,能降低模型误设的风险,还能便利地分析误差结构。     

单变量Bayes正态动态线性模型及其预测

Bayes预测和动态模型是20世纪70年代发展起来的一套新的时间序列分析方法,其中单变量Bayes正态动态线性模型(UBNDLM)在实际应用中最为常见和重要。在UBNDLM应用中,通常假定观测误差方差是未知常量,其值在建模的开始由估计给出。一般的做法是对具体的问题通过专家经验给出,并没有一个统一有效的办法。文章针对这一情形,给出了观测误差方差值一种简单易用的估计方法。同时也提供了数值试验说明新方法是有效的,这就给该类UBNDLM的应用带来了方便。     

Linear Transformations of Linear Mixed-Effects Models

A number of articles have discussed the way lower order polynomial and interaction terms should be handled in linear regression models. Only if all lower order terms are included in the model will the regression model be invariant with respect to coding transformations of the variables. If lower order terms are omitted, the regression model will not be well formulated. In this paper, we extend this work to examine the implications of the ordering of variables in the linear mixed-effects model. We demonstrate how linear transformations of the variables affect the model and tests of significance of fixed effects in the model. We show how the transformations modify the random effects in the model, as well as their covariance matrix and the value of the restricted log-likelihood. We suggest a variable selection strategy for the linear mixed-effects model.     

Estimation in Singular Linear Models with Stochastic Linear Restrictions and Linear Equality Restrictions

This article is concerned with the parameter estimation in a singular linear regression model with stochastic linear restrictions and linear equality restrictions simultaneously. A new estimator is introduced and it is proved that the proposed estimator is superior to the least squares estimator and singular mixed estimator in the mean squared error sense under certain conditions.     

Estimation in Singular Linear Models with Stochastic Linear Restrictions

This article generalizes the ordinary mixed estimator (OME) in theory, and obtains the estimator of the unknown regression parameters in singular linear models with stochastic linear restrictions: singular mixed estimator (SME). We also give some properties of SME obtained in this article, and prove that it is superior to unrestricted least squared estimator (LSE) in singular linear models in the sense of the covariance matrix and generalized mean square error (GMSE). After that, we also have a discussion about the two-stage estimator of SME. The result we give in this article could be regarded as generalizations of both OME and unrestricted LSE at the same time.     

Empirical Likelihood for Linear Models Under Linear Process Errors

In this article, we study the construction of confidence intervals for regression parameters in a linear model under linear process errors by using the blockwise technique. It is shown that the blockwise empirical likelihood (EL) ratio statistic is asymptotically χ²-type distributed. The result is used to obtain EL based confidence regions for regression parameters. The finite-sample performance of the method is evaluated through a simulation study.     

Power-Divergence Test Statistics for Testing Linear by Linear Association

Power-divergence test statistics have been considered to test linear by linear association for two-way contingency tables. These test statistics have been compared based on designed simulation study and asymptotic results for 2 × 2, 2 × 3, and 3 × 3 tables. According to the results, there are test statistics with better properties than the well-known likelihood ratio test statistic for small and moderate samples.     

线性GMDH参数模型的无偏估计研究

 多元线性回归分析中,参数无偏性是参数估计方法的一个重要指标。本文对线性GMDH参数模型建立多元线性模型进行了研究,得到以下结论：一,在满足经典线性回归模型的假设条件下,其参数估计量具有无偏的性质;二,在满足其它假设条件下,可以在样本量少于待估参数的情况下建模,估计的参数也是无偏的;三,用参数GMHD方法建模时,它对完全多重共线性是免疫的。     

Change Point Estimation of Multivariate Linear Profiles Under Linear Drift

In this paper, maximum likelihood estimators (MLE) for both step and linear drift changes in the regression parameters of multivariate linear profiles are developed. Performance of the proposed estimators is compared under linear drift changes in the regression parameters when a combined MEWMA and Chi-square control charts method signals an out-of-control condition. The effect of smoothing parameter of MEWMA control charts, missing data, and multiple drift changes on the performance of the both estimators is also evaluated. The application of the proposed estimators is also investigated thorough a numerical example resulted from a real case.     

Robust Linear Calibration

We regard the simple linear calibration problem where only the response y of the regression line y = β₀ + β₁ t is observed with errors. The experimental conditions t are observed without error. For the errors of the observations y we assume that there may be some gross errors providing outlying observations. This situation can be modeled by a conditionally contaminated regression model. In this model the classical calibration estimator based on the least squares estimator has an unbounded asymptotic bias. Therefore we introduce calibration estimators based on robust one-step-M-estimators which have a bounded asymptotic bias. For this class of estimators we discuss two problems: The optimal estimators and their corresponding optimal designs. We derive the locally optimal solutions and show that the maximin efficient designs for non-robust estimation and robust estimation coincide.     

Minimax Linear Smoothers

We consider the problem of estimating the mean of a multivariate distribution. As a general alternative to penalized least squares estimators, we consider minimax estimators for squared error over a restricted parameter space where the restriction is determined by the penalization term. For a quadratic penalty term, the minimax estimator among linear estimators can be found explicitly. It is shown that all symmetric linear smoothers with eigenvalues in the unit interval can be characterized as minimax linear estimators over a certain parameter space where the bias is bounded. The minimax linear estimator depends on smoothing parameters that must be estimated in practice. Using results in Kneip (1994), this can be done using Mallows' C _L -statistic and the resulting adaptive estimator is now asymptotically minimax linear. The minimax estimator is compared to the penalized least squares estimator both in finite samples and asymptotically.     

Generalized Linear Models

The importance of random number generators has increased over the years. This follows from the fact that contemporary research methods rely more and more on simulation and the increased importance of encryption technology. The output of a random number generator is created by either an algorithm or a physical device. The most popular method for random number generation is through the use of an algorithm. This article presents a new category of physical random bit generator that is packaged by several manufacturers. A statistical analysis of the output from the generators is given.