高维部分线性模型的变量选择和估计

考虑高维部分线性模型,提出了同时进行变量选择和估计兴趣参数的变量选择方法.将Dantzig变量选择应用到线性部分及非参数部分的各阶导数,从而获得参数和非参数部分的估计,且参数部分的估计具有稀疏性,证明了估计的非渐近理论界.最后,模拟研究了有限样本的性质.     

广义线性模型(九)

本讲座是广义线性模型这个题目的一个比较系统的介绍。主要分3部分:建模、统计分析与模型选择和诊断。写作时依据的主要参考资料是L.Fahrmeir等人的《MultivariateStatisticalMod elingBasedonGeneralizedLinearModels》。     

广义线性模型(五)

本讲座是广义线性模型这个题目的一个比较系统的介绍。主要分 3部分 :建模、统计分析与模型选择和诊断。写作时依据的主要参考资料是L .Fahrmeir等人的《MultivariateStatisticalModelingBasedonGeneralizedLinearModels》。     

广义线性模型(七)

本讲座是广义线性模型这个题目的一个比较系统的介绍。主要分3部分:建模、统计分析与模型选择和诊断。写作时依据的主要参考资料是L.Fahrmeir等人的《MultivariateStatisticalModelingBasedonGeneralizedLinearModels》。     

广义线性模型(四)

本讲座是广义线性模型这个题目的一个比较系统的介绍。主要分 3部分 ;建模、统计分析与模型选择和诊断。写作时依据的主要参考资料是L .Fahrmeir等人的《MultivariateStatisticalModelingBasedonGeneralizedLinearModels》。     

Generalized Partially Linear Measurement Error Models

This article considers generalized partially linear models when the linear covariate is measured with additive error. We propose estimators of parameter and nonparametric function by using local linear regression, the SIMEX technique, and generalized estimating equation. The asymptotic normality of the estimators of the parameter, and bias and variance of the estimators of the nonparametric component are derived under appropriate assumptions. In addition, the generalization to clustered measurements is discussed. The approaches are used to the analysis of data from the Framingham Heart Study. A simulation experiment is conducted for an illustration.     

纵向数据下非参数带测量误差的部分线性变系数模型的估计

本文研究纵向数据下非参数部分带有测量误差的部分线性变系数模型的估计.利用B样条函数近似模型中的变系数函数,构造偏差修正的二次推断函数,得到模型中未知参数和变系数函数的估计.证明变系数函数估计量的相合性和参数估计量的渐近正态性.数值模拟和实例分析结果表明所提估计方法在有限样本下的有效性.     

部分线性自回归模型中误差方差的核估计

基于非参数函数的核估计,构造了部分线性自回归模型中误差四阶矩的相合估计,从而给出了误差方差核估计的渐近正态性,并通过模拟算例和实例说明了其应用.     

Penalized Estimation in Large-Scale Generalized Linear Array Models

Large-scale generalized linear array models (GLAMs) can be challenging to fit. Computation and storage of its tensor product design matrix can be impossible due to time and memory constraints, and previously considered design matrix free algorithms do not scale well with the dimension of the parameter vector. A new design matrix free algorithm is proposed for computing the penalized maximum likelihood estimate for GLAMs, which, in particular, handles nondifferentiable penalty functions. The proposed algorithm is implemented and available via the R package glamlasso. It combines several ideas—previously considered separately—to obtain sparse estimates while at the same time efficiently exploiting the GLAM structure. In this article, the convergence of the algorithm is treated and the performance of its implementation is investigated and compared to that of glmnet on simulated as well as real data. It is shown that the computation time for glamlasso scales favorably with the size of the problem when compared to glmnet. Supplementary materials, in the form of R code, data and visualizations of results, are available online.     

A Flexible Model for Generalized Linear Regression with Measurement Error

This paper focuses on the question of specification of measurement error distribution and the distribution of true predictors in generalized linear models when the predictors are subject to measurement errors. The standard measurement error model typically assumes that the measurement error distribution and the distribution of covariates unobservable in the main study are normal. To make the model flexible enough we, instead, assume that the measurement error distribution is multivariate t and the distribution of true covariates is a finite mixture of normal densities. Likelihood–based method is developed to estimate the regression parameters. However, direct maximization of the marginal likelihood is numerically difficult. Thus as an alternative to it we apply the EM algorithm. This makes the computation of likelihood estimates feasible. The performance of the proposed model is investigated by simulation study.     

Statistical Inference for Partially Linear Regression Models with Measurement Errors

In this paper,the authors investigate three aspects of statistical inference for the partially linear regression models where some covariates are measured with errors.Firstly, a bandwidth selection procedure is proposed,which is a combination of the differencebased technique and GCV method.Secondly,a goodness-of-fit test procedure is proposed, which is an extension of the generalized likelihood technique.Thirdly,a variable selection procedure for the parametric part is provided based on the nonconcave penalization and corrected profile least squares.Same as＂Variable selection via nonconcave penalized likelihood and its oracle properties＂（J.Amer.Statist.Assoc.,96,2001,1348-1360）,it is shown that the resulting estimator has an oracle property with a proper choice of regularization parameters and penalty function.Simulation studies are conducted to illustrate the finite sample performances of the proposed procedures.     

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.     

广义线性回归极大似然估计的强相合性

设有该文第1节所描述的广义线性回归模型,以$\underline{\lambda}_n$和$\overline{\lambda}_n$分别记$\sum\limits_{i=1}^{n}Z_iZ_i^{\prime}$的最小和最大特征根,$\hat{\beta}_n$记$\beta_0$的极大似然估计.在文献[1]中,当\{$Z_i,i\ge1$\}有界时得到$\hat{\beta}_n$强相合的充分条件,在自然联系和非自然联系下分别为$\underline{\lambda}_n\rightarrow\infty$, $(\overline{\lambda}_n)^{1/2+\delta}=O(\underline{\lambda}_n)$（对某$\delta>0$)以及$\underline{\lambda}_n\rightarrow\infty$, $\overline{\lambda}_n=O(\underline{\lambda}_n)$.作者将后一结果改进为只要求$(\overline{\lambda}_n)^{1/2+\delta}=O(\underline{\lambda}_n)$,从而与自然联系情况下的条件达到一致.     

非寿险业务未决赔款准备金的两阶段广义线性模型估计

本文以非寿险业务未决赔款准备金估计的确定性方法-PPCI法的思想为基础,分两阶段建立广义线性模型,分别对索赔次数和已发生每案赔付额进行估计,进而得到未决赔款准备金的估计值,并对模型的预测误差进行估计。文中通过一个实例对所述方法进行验证,并从预测误差的角度与其它模型进行比较。最后对该模型特点进行了总结。     

广义线性模型(六)

本讲座是广义线性模型这个题目的一个比较系统的介绍。主要分 3部分 :建模、统计分析与模型选择和诊断。写作时依据的主要参考资料是L .Fahrmeir等人的 :《MultivariateStatisticalModel ingBasedonGeneralizedLinearModles》。     

部分线性自回归模型中误差方差伪最小二乘估计的渐近正态性

Consider the model Y_t=βY_t-1 g(Y_(t-2)) ε_t for 3＜=t＜=T.Here g is an unknown function,βis an unknown parameter,ε_t are i.i.d,random errors with mean 0 and varianceσ~2 and the fourth momentα_4,andε_t are independent of Y_s for all t＞=3 and s=1,2. Pseudo-LS estimators■_T~2,■4T and■_T~2 ofσ~s,α_4 and Var(ε_3~2)are respectively constructed based on piecewise polynomial approximator of g.The weak consistency of■4T and■_T~2 are proved.The asymptotic normality of■_T~2 is given,i.e.T~(1/2)(■_T~2-σ~2)/■_T converges in distribution to N(0,1).The result can be used to establish large sample interval estimates ofσ~2 or to make large sample tests forσ~2.     

含测量误差的部分线性模型的发散参数估计(英文)

本文考虑了部分线性模型中,线性部分协变量含有测量误差,并且线性部分的参数随着样本量的增大而发散的估计问题.我们考虑了用可观测的替代变量来替代不可观察到的真实变量,这种替代变量的期望与真实变量存在线性关系.我们提出了估计方法,并研究了估计量的相合性与渐进正态性.此外,我们研究了发散参数的发散速度.我们通过模拟来说明该估计的实际效果.     

Influence Analysis for Linear Measurement Error Models

In this paper, we present a unified diagnostic method for linear measurement error models based upon the corrected likelihood of Nakamura (1990, Biometrika, 77, 127–137). Both global influence and local influence are discussed. The case-deletion model and mean-shift outlier model are considered, and they are shown to be approximately equivalent. Several diagnostic measures are derived and discussed. It is found that they can be written in terms of the residual and leverage measure. Some existing results are improved. Numerical example illustrates that our method is useful for diagnosing influential observations.     

测量误差数据下线性模型的几乎无偏岭估计

文章讨论带测量误差的线性模型中参数估计的问题.当带测量误差的线性模型存在复共线的时候,通过几乎无偏估计的思想,提出了几乎无偏岭估计,并对估计的性质进行分析.通过研究发现几乎无偏岭估计不但能克服复共线性,同时有比较小的均方误差.