广义非参数回归的B样本贝叶斯估计

本文主要研究广义非参数模型B样条Bayes估计 .将回归函数按照B样条基展开 ,我们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B样条函数的后验均值估计回归函数 .并给出了回归函数B样条Bayes估计的MCMC的模拟计算方法 .通过对Logistic非参数回归的模拟研究 ,表明B样条Bayes估计得到了很好的估计效果     

变系数模型的Bayes样条估计

本文考察变系数模型y=x1β1(t) x2β2(t) … xpβp(t) ∈,∈-N(0,σ2),βr(t),r=1,…,P是光滑的连续函数.假定βr(t)是三阶的B样条函数,给结点的个数一个均匀先验,用贝叶斯模型平均的方法估计函数系数,这种估计方法充分考虑到各个函数系数的差别,允许不同的函数系数有不同的结点个数,即允许不同的函数系数使用不同的光滑参数.     

纵向数据下变系数测量误差模型的渐近估计

本文主要研究纵向数据下变系数测量误差模型的估计问题.利用B样条方法逼近模型中未知的变系数,构造关于B样条系数的二次推断函数来处理未知的个体内相关和测量误差,得到变系数的二次推断函数估计,建立估计方法和结果的渐近性质.数值模拟结果显示本文提出的估计方法具有一定的实用价值.     

变系数混合模型的光滑样条推断

为了拟合纵向数据和其他相关数据,本文提出了变系数混合效应模型(VCMM).该模型运用变系数线性部分来表示协变量对响应变量的影响,而用随机效应来描述纵向数据组内的相关性, 因此,该模型允许协变量和响应变量之间存在十分灵活的泛函关系.文中运用光滑样条来估计均值部分的系数函数,而用限制最大似然的方法同时估计出光滑参数和方差成分,我们还得到了所提估计的计算方法.大量的模拟研究表明对于具有各种协方差结构的变系数混合效应模型,运用本文所提出的方法都能够十分有效地估计出模型中的系数函数和方差成分.     

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.     

纵向数据广义部分线性模型的惩罚GMM估计

对纵向数据的部分线性模型,通常的做法是用样条方法或者核方法逼近非参数部分,然后再用广义估计方程的估计方法去估计参数部分.本文使用P-样条拟合非参数函数,对不同的矩条件用不同的广义矩方法对模型的参数和非参数进行估计,并且给出了估计量的大样本性质;并用计算机模拟和实例证明了当模型中存在不同的矩条件时,采用不同的惩罚广义矩方法可以显著地提高估计精度.     

变系数模型的小波估计

变系数模型是近年来文献中经常出现的一种统计模型.本文主要研究了变系数模型的估计问题,提出运用小波的方法估计变系数模型中的系数函数,小波估计的优点是避免了象核估计、光滑样条等传统的变系数模型估计方法对系数函数光滑性的一些严格限制. 并且,我们还得到了小波估计的收敛速度和渐近正态性.模拟研究表明变系数模型的小波估计有很好的估计效果.     

变系数测量误差模型的B-样条估计(英文)

本文考虑变系数测量误差模型的估计问题,得到该模型变系数函数修正的最小二乘B-样条估计,同时得到非参数函数估计的最优收敛速度.模拟结果表明该方法是有效的.     

部分函数线性变系数模型的样条估计及其应用

本文针对Tecator数据介绍一种新的模型一部分函数线性变系数模型,并基于样条估计方法得到了模型中未知系数函数的估计,同时在适当的条件下给出了系数函数估计及模型均方预测误差的收敛速度。通过数值模拟说明本文所提估计方法的有效性。最后基于该模型对Tecator数据进行了统计分析。     

针对面板数据的半参数变系数可加模型的估计和推断

本文研究针对面板数据的半参数变系数可加模型的估计和推断问题,该模型将因变量与自变量之间的关系建模成未知函数的形式,并且假设它们之间的关系是随时间变化的.本文基于B样条方法估计未知的参数和函数.本文在允许(N,T)→∞的情况下建立各个估计量的渐近性质.通过大量的模拟评估所提出的估计方法的表现.最后,本文将所推荐的模型用于调查Fama-French三因子的时变行为.     

Bayesian Variable Selection for Median Regression

When the data has heavy tail feature or contains outliers, conventional variable selection methods based on penalized least squares or likelihood functions perform poorly. Based on Bayesian inference method, we study the Bayesian variable selection problem for median linear models. The Bayesian estimation method is proposed by using Bayesian model selection theory and Bayesian estimation method through selecting the Spike and Slab prior for regression coefficients, and the effective posterior Gibbs sampling procedure is also given. Extensive numerical simulations and Boston house price data analysis are used to illustrate the effectiveness of the proposed method.     

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??When the data has heavy tail feature or contains outliers, conventional variable selection methods based on penalized least squares or likelihood functions perform poorly. Based on Bayesian inference method, we study the Bayesian variable selection problem for median linear models. The Bayesian estimation method is proposed by using Bayesian model selection theory and Bayesian estimation method through selecting the Spike and Slab prior for regression coefficients, and the effective posterior Gibbs sampling procedure is also given. Extensive numerical simulations and Boston house price data analysis are used to illustrate the effectiveness of the proposed method.     

Estimating structural credit risk models when market prices are contaminated with noise

In this paper, sequential estimation on hidden asset value and model parameter estimation is implemented under the Black–Cox model. To capture short‐term autocorrelation in the stock market, we assume that market noise follows a mean reverting process. For estimation, Bayesian methods are applied in this paper: the particle filter algorithm for sequential estimation of asset value and the generalized Gibbs and multivariate adapted Metropolis methods for model parameters estimation. The first simulation study shows that sequential hidden asset value estimation using both option price and equity price is more efficient than estimation using equity price alone. The second simulation study shows that, by applying the generalized Gibbs sampling and multivariate adapted Metropolis methods, model parameters can be estimated successfully. In an empirical analysis, the stock market noise for firms with more liquid stock is estimated as having smaller volatility. Copyright © 2015 John Wiley & Sons, Ltd.     

Bayesian Ising Graphical Model for Variable Selection

In this article, we propose a new Bayesian variable selection (BVS) approach via the graphical model and the Ising model, which we refer to as the “Bayesian Ising graphical model” (BIGM). The BIGM is developed by showing that the BVS problem based on the linear regression model can be considered as a complete graph and described by an Ising model with random interactions. There are several advantages of our BIGM: it is easy to (i) employ the single-site updating and cluster updating algorithm, both of which are suitable for problems with small sample sizes and a larger number of variables, (ii) extend this approach to nonparametric regression models, and (iii) incorporate graphical prior information. In our BIGM, the interactions are determined by the linear model coefficients, so we systematically study the performance of different scale normal mixture priors for the model coefficients by adopting the global-local shrinkage strategy. Our results indicate that the best prior for the model coefficients in terms of variable selection should place substantial weight on small, nonzero shrinkage. The methods are illustrated with simulated and real data. Supplementary materials for this article are available online.     

Generalized ridge regression,least squares with stochastic prior information,and Bayesian estimators

The ridge estimator of the usual linear model is generalized by the introduction of an a priori vector r and an associated positive semidefinite matrix S. It is then shown that the generalized ridge estimator can be justified in two ways: (a) by the minimization of the residual sum of squares subject to a constraint on the length, in the metric S, of the vector of differences between r and the estimated linear model coefficients, (b) by incorporating prior knowledge, r playing the role of the vector of means and S proportional to the precision matrix. Both a Bayesian and an Aitken generalized least squares frameworks are used for the latter. The properties of the new estimator are derived and compared to the ordinary least squares estimator. The new method is illustrated with different assumptions on the form of the S matrix.     

纵向数据下半参数联合均值协方差模型的贝叶斯分析

基于改进的Cholesky分解,研究分析了纵向数据下半参数联合均值协方差模型的贝叶斯估计和贝叶斯统计诊断,其中非参数部分采用B样条逼近.主要通过应用Gibbs抽样和Metropolis-Hastings算法相结合的混合算法获得模型中未知参数的贝叶斯估计和贝叶斯数据删除影响诊断统计量.并利用诊断统计量的大小来识别数据的异常点.模拟研究和实例分析都表明提出的贝叶斯估计和诊断方法是可行有效的.     

Spatially Adaptive Bayesian Penalized Regression Splines (P-splines)

In this article we study penalized regression splines (P-splines), which are low-order basis splines with a penalty to avoid undersmoothing. Such P-splines are typically not spatially adaptive, and hence can have trouble when functions are varying rapidly. Our approach is to model the penalty parameter inherent in the P-spline method as a heteroscedastic regression function. We develop a full Bayesian hierarchical structure to do this and use Markov chain Monte Carlo techniques for drawing random samples from the posterior for inference. The advantage of using a Bayesian approach to P-splines is that it allows for simultaneous estimation of the smooth functions and the underlying penalty curve in addition to providing uncertainty intervals of the estimated curve. The Bayesian credible intervals obtained for the estimated curve are shown to have pointwise coverage probabilities close to nominal. The method is extended to additive models with simultaneous spline-based penalty functions for the unknown functions. In simulations, the approach achieves very competitive performance with the current best frequentist P-spline method in terms of frequentist mean squared error and coverage probabilities of the credible intervals, and performs better than some of the other Bayesian methods.     

Bayesian approaches for analyzing earthquake catastrophic risk

Extreme value theory has been widely used in analyzing catastrophic risk. The theory mentioned that the generalized Pareto distribution (GPD) could be used to estimate the limiting distribution of the excess value over a certain threshold; thus the tail behaviors are analyzed. However, the central behavior is important because it may affect the estimation of model parameters in GPD, and the evaluation of catastrophic insurance premiums also depends on the central behavior. This paper proposes four mixture models to model earthquake catastrophic loss and proposes Bayesian approaches to estimate the unknown parameters and the threshold in these mixture models. MCMC methods are used to calculate the Bayesian estimates of model parameters, and deviance information criterion values are obtained for model comparison. The earthquake loss of Yunnan province is analyzed to illustrate the proposed methods. Results show that the estimation of the threshold and the shape and scale of GPD are quite different. Value-at-risk and expected shortfall for the proposed mixture models are calculated under different confidence levels.     

Reliability analysis for Weibull distribution with homogeneous heavily censored data based on Bayesian and least-squares methods

The reliability for Weibull distribution with homogeneous heavily censored data is analyzed in this study. The universal model of heavily censored data and existing methods, including maximum likelihood, least-squares, E-Bayesian estimation, and hierarchical Bayesian methods, are introduced. An improved method is proposed based on Bayesian inference and least-squares method. In this method, the Bayes estimations of failure probabilities are focused on for all the samples. The conjugate prior distribution of failure probability is set, and an optimization model is developed by maximizing the information entropy of prior distribution to determine the hyper-parameters. By integrating the likelihood function, the posterior distribution of failure probability is then derived to yield the Bayes estimation of failure probability. The estimations of reliability parameters are obtained by fitting distribution curve using least-squares method. The four existing methods are compared with the proposed method in terms of applicability, precision, efficiency, robustness, and simplicity. Specifically, the closed form expressions concerning E-Bayesian estimation and hierarchical Bayesian methods are derived and used. The comparisons demonstrate that the improved method is superior. Finally, three illustrative examples are presented to show the application of the proposed method.     

An innovative Bayesian sequential censored sampling inspection method and application to test design

This paper proposes an innovative Bayesian sequential censored sampling inspection method to improve the inspection level and reduce the sample size in acceptance test plans for continuous lots. A mathematical model of Bayesian sequential censored sampling is built, where a new inspection parameter is created and two types of risk are modified. As the core of Bayesian risk formulas, a new structure method of the prior distribution is presented by combining the empirical distribution with the uncertainty of the estimation. To improve the fitting accuracy of parameter estimation, an adaptive genetic algorithm is applied and compared with different parameter estimation methods. In the prior distribution, a prior estimator is introduced to design a sampling plan for continuous lots. Then, three types of producer's and consumer's risks are derived and compared. The simulation results indicate that the modified Bayesian sampling method performs well, with the lowest risks and the smallest sample size. Finally, a new sequential censored sampling plan for continuous lots is designed for the accuracy acceptance test of an aircraft. The test results show that compared with the traditional single sampling plan, the sample size is reduced by 66.7%, saving a vast amount of test costs.