半参数混合效应模型中的估计及其强相合性

将Tao等(1999)提出的线性混合效应模型推广为半参数混合效应模型,给出了模型参数、回归函数和随机效应密度的估计,并研究了估计的强相合性及部分强相合速度.统计模拟表明我们给出的估计方法是可行的.     

一类零膨胀半参数混合效应模型的惩罚似然估计

本文将半参数线性混合效应模型推广应用到一类具有零膨胀的纵向数据或集群数据的研究中,提出了一类新的半参数混合效应模型,然后利用广义交叉核实法选取光滑参数,通过最大惩罚似然函数方法与EM算法给出了模型参数部分与非参数部分的估计方法,最后,通过模拟和实例说明了本文方法的有效性.     

带有二元连接函数的半参数模型

提出了一种新的带有二元连接函数的广义半参数模型,即二元连接模型(简称为BLM).使用轮廓似然方法估计模型的参数和非参数部分,并给出了计算算法.证明了所得的未知参数的估计量为n~(1/2)-相合,渐近正态且具有渐近最小方差,给出了实际数据分析和模拟研究,最终采用局部功效方法来检验非参数部分的线性性.     

半参数再生散度非线性模型中参数的投影核和刀切估计的相合性与渐近正态性

半参数再生散度非线性模型(SRDNM)是再生散度非线性模型和半参数回归模型的自然推广和发展,它包括半参数非线性模型和半参数广义线性模型等特殊模型. 基于非参数部分的局部核估计, 给出了SRDNM模型中参数的投影核估计与刀切估计, 并对其进行了理论比较. 在一定的正则条件下,得到了这两类估计的强相合性与渐近正态性. 相比之下, 刀切估计比投影核估计具有更大的渐近方差. 最后, 模拟研究和实例分析被用来说明所给方法的有效性.     

半参数广义线性混合效应模型的影响分析

本文把随机效应当作是缺失数据并利用P-样条拟合非参数部分,从而得到了半参数广义线性混合效应模型(GPLMM)的MCNR估计算法;同时利用Q-函数,我们得到了模型的参数部分的广义Cook距离以及非参数部分的广义DFIT,此外,本文还研究了四种不同扰动情形的PLMM的局部影响分析,得到了相应的影响矩阵,最后,我们通过—个实际例子验证了所提出的诊断统计量的有效性。     

部分线性混合效应模型中方差分量的稳健估计

部分线性混合效应模型中方差分量是我们感兴趣的参数, 文献中已经给出许多估计方法. 但是其中很多方法都可以归结为广义估计方程方法(GEE), 如: 最大似然估计(MLE), 约束最大似然估计(REMLE)等, 而GEE方法对异常点很敏感. 本文提出一组关于部分线性混合效应模型(PLMM)中均值和方差分量的稳健估计方程, 对均值和方差分量同时进行稳健估计; 并进行了随机模拟考察所提出稳健估计的有效性, 最后通过两个实例, 说明了所提方法的可行性.     

纵向数据半参数混合效应模型中的估计方法

本文将Tao等(1999)提出的线性混合效应模型推广为半参数混合效应模型,给出了模型参数、回归函数和随机效应密度的估计,并研究了估计的渐近性质.统计模拟表明我们给出的估计方法是可行的.     

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。     

具有自相关误差结构的面板数据部分线性单指标模型的统计推断

部分线性单指标模型是在科学研究中具有广泛应用的经典半参数模型之一.本文主要研究具有自相关误差结构的面板数据的部分线性单指标模型的统计推断问题.通过结合局部多项式和纠偏广义估计方程方法,本文提出模型参数的可行加权广义估计(feasible weighted generalized estimating equation estimation, GEE-FW),证明该估计具有相合性和渐近正态性,并且在渐近方差意义下阐明该估计比工作独立的广义估计(generalized estimating equation estimation based on working independence,GEE-WI)更加有效.此外,本文对模型中未知连接函数提出两阶段局部线性估计(two step local linear generalized estimating equation estimation, GEE-TS),建立该估计的渐近性质.数值模拟研究和实际数据分析都表明了本文所提出的方法是有效的,在理论和应用方面均具有良好的表现.     

平衡数据结构下ANOVA 估计和SD 估计的比较

在线性混合效应模型下, 方差分析(ANOVA) 估计和谱分解(SD) 估计对构造精确检验和广义P-值枢轴量起着非常重要的作用. 尽管这两估计分别基于不同的方法, 但它们共享许多类似的优点, 如无偏性和有精确的表达式等. 本文借助于已得到的协方差阵的谱分解结果, 揭示了平衡数据一般线性混合效应模型下ANOVA 估计与SD 估计的关系, 并分别针对协方差阵两种结构: 套结构和多项分类随机效应结构, 给出了ANOVA 估计与SD 估计等价的充分必要条件.     

检验两个部分线性模型中非参函数相等

We propose the test statistic to check whether the nonparametric func-tions in two partially linear models are equality or not in this paper. We estimate the nonparametric function both in null hypothesis and the alternative by the local linear method, where we ignore the parametric components, and then estimate the parameters by the two stage method. The test statistic is derived, and it is shown to be asymptotically normal under the null hypothesis.     

半参数变系数部分线性模型的统计推断

本文在多种复杂数据下, 研究一类半参数变系数部分线性模型的统计推断理论和方法. 首先在纵向数据和测量误差数据等复杂数据下, 研究半参数变系数部分线性模型的经验似然推断问题, 分别提出分组的和纠偏的经验似然方法. 该方法可以有效地处理纵向数据的组内相关性给构造经验似然比函数所带来的困难. 其次在测量误差数据和缺失数据等复杂数据下, 研究模型的变量选择问题, 分别提出一个“纠偏” 的和基于借补值的变量选择方法. 该变量选择方法可以同时选择参数分量及非参数分量中的重要变量, 并且变量选择与回归系数的估计同时进行. 通过选择适当的惩罚参数, 证明该变量选择方法可以相合地识别出真实模型, 并且所得的正则估计具有oracle 性质.     

Model averaging for semiparametric additive partial linear models

To improve the prediction accuracy of semiparametric additive partial linear models(APLM) and the coverage probability of confidence intervals of the parameters of interest,we explore a focused information criterion for model selection among ALPM after we estimate the nonparametric functions by the polynomial spline smoothing,and introduce a general model average estimator.The major advantage of the proposed procedures is that iterative backfitting implementation is avoided,which thus results in gains in co...     

多元部分线性模型的B-样条估计(英文)

本文考虑多元部分线性回归模型的估计问题,得到了该模型参数的最小二乘估计和非参数函数的B-样条估计,并证明了参数估计的渐近正态性,给出了非参数函数估计的最优收敛速度.     

Checking the adequacy of partial linear models with missing covariates at random

In this paper, we consider the goodness-of-fit for checking whether the nonparametric function in a partial linear regression model with missing covariate at random is a parametric one or not. We estimate the selection probability by using parametric and nonparametric approaches. Two score type tests are constructed with the estimated selection probability. The asymptotic distributions of the test statistics are investigated under the null and local alterative hypothesis. Simulation studies are carried out to examine the finite sample performance of the sizes and powers of the tests. We apply the proposed procedure to a data set on the AIDS clinical trial group (ACTG 315) study.     

A Frisch-Newton Algorithm for Sparse Quantile Regression

Recent experience has shown that interior-point methods using a log barrier approach are far superior to classical simplex methods for computing solutions to large parametric quantile regression problems. In many large empirical applications, the design matrix has a very sparse structure. A typical example is the classical fixed-effect model for panel data where the parametric dimension of the model can be quite large, but the number of non-zero elements is quite small. Adopting recent developments in sparse linear algebra we introduce a modified version of the Prisch-Newton algorithm for quantile regression described in Portnoy and Koenker~([28]). The new algorithm substantially reduces the storage (memory) requirements and increases computational speed. The modified algorithm also facilitates the development of nonparametric quantile regression methods. The pseudo design matrices employed in nonparametric quantile regression smoothing are inherently sparse in both the fidelity and roughness penalty components. Exploiting the sparse structure of these problems opens up a whole range of new possibilities for multivariate smoothing on large data sets via ANOVA-type decomposition and partial linear models.     

Automatic model selection for partially linear models

We propose and study a unified procedure for variable selection in partially linear models. A new type of double-penalized least squares is formulated, using the smoothing spline to estimate the nonparametric part and applying a shrinkage penalty on parametric components to achieve model parsimony. Theoretically we show that, with proper choices of the smoothing and regularization parameters, the proposed procedure can be as efficient as the oracle estimator [J. Fan, R. Li, Variable selection via nonconcave penalized likelihood and its oracle properties, Journal of American Statistical Association 96 (2001) 1348–1360]. We also study the asymptotic properties of the estimator when the number of parametric effects diverges with the sample size. Frequentist and Bayesian estimates of the covariance and confidence intervals are derived for the estimators. One great advantage of this procedure is its linear mixed model (LMM) representation, which greatly facilitates its implementation by using standard statistical software. Furthermore, the LMM framework enables one to treat the smoothing parameter as a variance component and hence conveniently estimate it together with other regression coefficients. Extensive numerical studies are conducted to demonstrate the effective performance of the proposed procedure.     

带有不可忽略缺失数据的半参数再生散度模型的贝叶斯分析

半参数再生散度模型是再生散度模型和半参数回归模型的推广,包括了半参数广义线性模型和广义部分线性模型等特殊类型.讨论的是该模型在响应变量和协变量均存在非随机缺失数据情形下参数的Bayes估计和基于Bayes因子的模型选择问题.在分析中,采用了惩罚样条来估计模型中的非参数成分,并建立了Bayes层次模型;为了解决Gibbs抽样过程中因参数高度相关带来的混合性差以及因维数增加导致出现不稳定性的问题,引入了潜变量做为添加数据并应用了压缩Gibbs抽样方法,改进了收敛性;同时,为了避免计算多重积分,利用了M-H算法估计边缘密度函数后计算Bayes因子,为模型的选择比较提供了一种准则.最后,通过模拟和实例验证了所给方法的有效性.     

Generalized partially linear mixed-effects models incorporating mismeasured covariates

In this article we consider a semiparametric generalized mixed-effects model, and propose combining local linear regression, and penalized quasilikelihood and local quasilikelihood techniques to estimate both population and individual parameters and nonparametric curves. The proposed estimators take into account the local correlation structure of the longitudinal data. We establish normality for the estimators of the parameter and asymptotic expansion for the estimators of the nonparametric part. For practical implementation, we propose an appropriate algorithm. We also consider the measurement error problem in covariates in our model, and suggest a strategy for adjusting the effects of measurement errors. We apply the proposed models and methods to study the relation between virologic and immunologic responses in AIDS clinical trials, in which virologic response is classified into binary variables. A dataset from an AIDS clinical study is analyzed.