广义变系数模型的Bayesian B样条估计

提出了广义变系数模型函数系数的一种新的估计方法．我们用B样条函数逼近函数系数,不具体选择节点的个数,而是节点个数取均匀的无信息先验,样条函数系数取正态先验,用Bayesian模型平均的方法估计各个函数系数．这种估计方法一个主要特点是允许各个函数系数所需节点个数的后验分布不同,因此允许不同函数系数使用不同的光滑参数．另外,本文还给出了Bayesian B样条估计的计算方法,并通过模拟例子,说明广义变系数模型的函数系数可以由Bayesian B样条估计方法得到很好的估计．     

关于“一类非参数回归函数估计性质”的注记

《应用数学》第三卷(1990)第四期刊载秦永松同志的“一类非参数回归函数估计的性质”一文,该文定理证明欠周全. 考察文[1]中定理1的证明:关于原文(8)式,即(原文中,上式漏掉因子(h_(n1)h_(n2))~(-1),这可以前后文对照发现).原文关于上式的证明有误.为了证明上式,原文证明了     

相依样本下非参数回归函数递推型核估计的渐近分布

设（Ｘｉ，Ｙｉ）１≤ｉ≤ｎ为来自二元总体（Ｘ，Ｙ）的平稳，φ－混合样本，记ｍ（ｘ）△Ｅ（Ｙ│Ｘ＝ｘ），ｍ（ｘ）的一种递推型核估计为ｍｎ（ｘ）＝ｎ∑ｉ＝１ｈｉ＾－１Ｙｉｋ（（ｘ－Ｘｉ）／ｈｉ）／ｎ∑ｊ＝１ｈ＾－１ｊｋ（ｘ－Ｘｊ）／ｈｊ）。本文在一定的条件下证明了（ｎ／（ｎ∑ｊ＝１ｈ＾－１ｊ）＾１／２）（ｍｎ（ｘ１）－ｍ（ｘ１），ｍｎ（ｘ２）－ｍ（ｘ２），．．．ｍｎ（ｘｒ０）－ｍ（ｘｒ０））′依分布收     

混合样本下非参数回归模型误差的矩相合估计

要考虑非参数回归模型Yi=g(Xi) εi，i=1，2…其中误差（ε，ii≥1)为φ混合随机变量列，且有共同的未知密度f(x)，g(x)=E(Y|X=x)为未知的回归函数，本由基于g(x)的非参数估计gn（x）定义的残差，然后再由基于残差构造的f(x)的估计fn(x)，在适当条件下，证明了fn(x)具有r(1相似文献   

NA样本回归函数估计的强相合性

在ＮＡ相依样本下研究非参数回归函数加权核估计的相合性,获得了一些较弱的充分条件,与此同时对ＮＡ序列给出一个简洁实用的Ｂｅｒｎｓｔｅｉｎ型不等式。     

一种基于样条方法的非参数回归的强相合估计

其中(X,Y)为二元随机变量,E(e|X)=0 a.s.设(X_i,Y_i),i=1,…,n为(X,Y)的n个独立观察值,我们的目的是寻找一个回归函数G(X)的相合估计。 对于这个问题的讨论,已经相当深入。目前主要集中在权函数法,这方面的结果可见[8],[9],[10],但是我们应该指出的是,在权函数法中所使用的权函数大都是人为选定的。例如核函数法,近邻方法。即使在使用cross-validation技术,也只是在于选择窗     

一类非参数回归函数估计的性质

设Z_(11),z_(12),…,Z_是在固定点(x_i,y_1),1≤≤n_1,1≤j≤n_2,的n_1n_2个观察值,适合模型 Z_(ij)=g(x_i,y_j)+ε_(ij),1≤i≤n_1,1≤j≤n_2。(1) 本文给出了g的一种估计并讨论了估计的性质。     

NA样本下非指数分布族参数的经验Bayes估计

在\"平方损失\"下,研究了基于NA样本情形下非指数分布族参数θ的经验Bayes估计.利用概率密度函数的核估计,构造了参数的经验Bayes(EB)估计量,在适当的条件下证明了获得的(EB)估计是渐近最优的且收敛速度的阶为O(n~(-(rs-2)/2(s+2))),其中s2,s∈N,2/sr1.最后给出一个满足定理条件的例子.     

相依样本下非参数回归函数估计的强收敛速度

设(X,Y),(X_1,Y_1,),…,(X_n,Y_n)是一个平稳、φ—混合过程((X,Y)∈R~d×R,E|Y|~(s δ)<∞,s≥2,δ>0),用m(x)记E{Y|X=x},本文讨论了m(x)的如下估计m_n(x)的强收敛速度:     

截尾数据下非参数回归函数核估计的强收敛速度

本文考虑在右侧随机截尾模型下，非参数回归函数核估计的强收敛问题，在一组自然的条件下，得到了与完全样本情况相当的收敛速度。     

半参数可加模型的广义Liu估计

作为部分线性模型和可加模型的推广,半参数可加模型在统计建模中应用广泛.考虑这类半参数模型在线性部分自变量存在共线性时的估计问题.基于Profile最小二乘方法,提出了参数分量的广义Profile-Liu估计,并给出了该估计量的偏和方差以及均方误差.最后利用数值模拟验证了所提方法的有效性.     

Robust Estimation for Generalized Additive Models

This article studies M-type estimators for fitting robust generalized additive models in the presence of anomalous data. A new theoretical construct is developed to connect the costly M-type estimation with least-squares type calculations. Its asymptotic properties are studied and used to motivate a computational algorithm. The main idea is to decompose the overall M-type estimation problem into a sequence of well-studied conventional additive model fittings. The resulting algorithm is fast and stable, can be paired with different nonparametric smoothers, and can also be applied to cases with multiple covariates. As another contribution of this article, automatic methods for smoothing parameter selection are proposed. These methods are designed to be resistant to outliers. The empirical performance of the proposed methodology is illustrated via both simulation experiments and real data analysis. Supplementary materials are available online.     

Fully Bayesian Analysis of Switching Gaussian State Space Models

In the present paper we study switching state space models from a Bayesian point of view. We discuss various MCMC methods for Bayesian estimation, among them unconstrained Gibbs sampling, constrained sampling and permutation sampling. We address in detail the problem of unidentifiability, and discuss potential information available from an unidentified model. Furthermore the paper discusses issues in model selection such as selecting the number of states or testing for the presence of Markov switching heterogeneity. The model likelihoods of all possible hypotheses are estimated by using the method of bridge sampling. We conclude the paper with applications to simulated data as well as to modelling the U.S./U.K. real exchange rate.     

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.     

不等式约束条件下部分线性回归模型的参数估计

本文研究了不等式约束条件下部分线性回归模型的参数估计问题,利用最优化方法和贝叶斯方法,给出了不等式约束条件下部分线性回归模型的最小二乘核估计和最佳贝叶斯估计,并且证明了在一定条件下,带约束条件的最小二乘核估计在均方误差意义下要优于无约束条件的最小二乘核估计。     

基于MCMC算法的贝叶斯变结构分位自回归模型研究

为了更全面细致的刻画时间序列变结构性的特征及其相依性,提出了一类马尔可夫变结构分位自回归模型。利用非对称Laplace分布构建了模型的似然函数,证明了当回归系数的先验分布选择为扩散先验分布时,参数的各阶后验矩都是存在的,并给出了能确定变点位置和性质的隐含变量的后验完全条件分布。仿真分析结果发现马尔可夫变结构分位自回归模型可以全面有效地实现对时间序列数据变结构性的刻画。并应用贝叶斯Markov分位自回归方法分析了中国证券市场的变结构性,结果发现中国证券市场在不同阶段尾部表现出不同的相依性。     

Generalized Moment Theory and Bayesian Robustness Analysis for Hierarchical Mixture Models

In applications of Bayesian analysis one problem that arises is the evaluation of the sensitivity, or robustness, of the adopted inferential procedure with respect to the components of the formulated statistical model. In particular, it is of interest to study robustness with respect to the prior, when this latter cannot be uniquely elicitated, but a whole class Γ of probability measures, agreeing with the available information, can be identified. In this situation, the analysis of robustness consists of finding the extrema of posterior functionals under Γ. In this paper, we provide a theoretical framework for the treatment of a global robustness problem in the context of hierarchical mixture modeling, where the mixing distribution is a random probability whose law belongs to a generalized moment class Γ. Under suitable conditions on the functions describing the problem, the solution of this latter coincides with the solution of a linear semi-infinite programming problem.     

Small Noise Asymptotics of the Bayesian Estimator in Nonidentifiable Models

We study the asymptotic behavior of the Bayesian estimator for a deterministic signal in additive Gaussian white noise, in the case where the set of minima of the Kullback–Leibler information is a submanifold of the parameter space. This problem includes as a special case the study of the asymptotic behavior of the nonlinear filter, when the state equation is noise-free, and when the limiting deterministic system is nonobservable. As the noise intensity goes to zero, the posterior probability distribution of the parameter asymptotically concentrates on the submanifold of minima of the Kullback–Leibler information. We give an explicit expression of the limit, and we study the rate of convergence. We apply these results to a practical example where nonidentifiability occurs.     

混合双参数广义Pareto分布的参数估计

Pareto分布族因其厚尾特点,在金融分析、寿命分析中都是非常重要的统计模型.但是对于混合双参广义Pareto分布,在模型参数估计时,传统的矩法估计和极大似然估计在理论上可以实现,实践时比较困难.本文应用EM算法之ECM算法,研究了混合广义Pareto分布在完全数据场合下的参数估计问题,并模拟说明EM算法来估计混合广义Pareto分布是一种容易实现又非常有效的方法.