一种检验回归参数差异的新方法

对回归模型的参数进行比较是计量经济学研究的一个重要内容.文章提出了一种新的思路来对回归模型的参数的差异进行检验,该方法与一般人们所用的Wald统计量来检验的方法和使用虚拟变量的方法相比而言比较灵活,应用面较广,它既可以对同一个回归方程的不同参数的差异进行比较,也可以对两个解释变量个数不同的回归方程的不同参数进行比较,在一定程度上能够解决其他方法所不能够处理的问题.     

超高维数据下部分线性可加分位数回归模型的变量选择

在超高维数据中,一方面,协变量的维数可能远远大于样本量,甚至随着样本量以指数级的速度增长;另一方面,超高维数据通常是异质的,协变量对条件分布中心的影响可能与他们对尾部的影响大不相同,甚至会出现重尾以及异常点的复杂情况。文章在协变量维度发散且为超高维的情况下研究了部分线性可加分位数回归模型的变量选择和稳健估计问题。首先,为了实现模型的稀疏性和非参数光滑性,引入了一种非凸Atan双惩罚,并采用分位迭代坐标下降算法来解决所提方法的优化问题。在选择适当正则化参数的情况下,证明了所提双惩罚估计量的理论性质。其次,通过模拟研究对所提方法的性能进行验证。模拟结果表明,所提方法比其他惩罚方法具有更好的表现,尤其是在数据存在重尾的情况下。最后,通过基于癌症筛查病人血液样本数据的实证来验证所提方法的实用性。     

传统数据发掘方法的缺陷

由于关于社会经济方面的数据无法经由实验得到,而只能被动地通过观察、观测获得,所以如何使用这有限的数据来发掘出隐藏在背后的社会经济规律是至关重要的.现在常用的方法是运用统计中的回归分析方法,在多个变量之间回归方程,以试图发现其中的社会经济规律.但是,一般来说,社会经济理论并未明确指定应该包括哪些变量,不包括哪些变量.这就导致建模者面对可能的变量的集合,要从这些“候选”变量中进行筛选,拟合大量的回归方程.这些回归方程随设定的不同而不同,随所用的独立解释变量的不同而不同.建模者要按照一定的准则选择“最优”或“成功”的模型来报告.“最优”或     

基于贝叶斯网稀疏结构学习的信用影响因素结构发现

面对海量高维信用数据,传统贝叶斯网络在刻画变量复杂结构和概率关系时遇到了挑战。尝试将基于multi-logit回归的离散贝叶斯网络稀疏方法用于个人信用影响因素结构关系的发现,实现从多维变量复杂关系中抓取重要结构关系;基于解路径探讨了用于结构发现的稀疏贝叶斯网络模型的选择标准,并比较了稀疏贝叶斯网络与经典贝叶斯网络结构学习的性能;结合领域先验知识进一步改进贝叶斯网络结构,定性分析多维变量存在的主要结构关系;在确定多维变量稀疏网络结构的基础上,采用贝叶斯后验估计获取模型参数,并利用贝叶斯网络推理定量分析关键变量对信贷客户类型的直接或间接影响。     

独立总体均值多重比较方法之新探

多个独立总体的均值多重比较是统计假设检验的一项重要内容.文章从虚拟变量回归的角度对此进行了考察,借助于其能够处理定性因素的特点,设计了一种新的方法来进行多个独立总体的均值的多重比较.首先阐述了虚拟变量回归替代单因素方差分析F检验的背景思路;然后从数学上论证了虚拟变量回归与单因素方差分析的等效性;接着阐述了虚拟变量回归进行均值比较的特点;最后提出了基于虚拟变量回归的进行多个独立总体的均值多重比较的方法.     

对应分析方法在大学毕业生就业因素分析中的应用

一、对应分析方法 对应分析方法是近年来发展起来的一种多元相依变量统计分析技术，它通过分析由定性数据构成的交互汇总表来揭示变量间的联系。当用变量的一系列类别分布图来描述变量之间的联系时，使用这一技术可以揭示同一变量各个类别之间的差异以及不同变量各个类别之间的对应关系。它不仅可以分析定性数据，同时还可以分析非线性关系。当我们分析的变量是定性数据，变量之间又存在非线性关系时，则可以用对应分析来揭示变量之间的联系。对应分析的基本形式是对由两个定性变量构成的交互表进行分析．将定性数据转变为可度量的分值，减…     

大数据背景下网络调查样本的建模推断问题研究——以广义Boosted模型的倾向得分推断为例

随着大数据和网络的不断发展,网络调查越来越广泛,大部分网络调查样本属于非概率样本,难以采用传统的抽样推断理论进行推断,如何解决网络调查样本的推断问题是大数据背景下网络调查发展的迫切需求。本文首次从建模的角度提出了解决该问题的基本思路：一是入样概率的建模推断,可以考虑构建基于机器学习与变量选择的倾向得分模型来估计入样概率推断总体;二是目标变量的建模推断,可以考虑直接对目标变量建立参数、非参数或半参数超总体模型进行估计;三是入样概率与目标变量的双重建模推断,可以考虑进行倾向得分模型与超总体模型的加权估计与混合推断。最后,以基于广义Boosted模型的入样概率建模推断为例演示了具体解决方法。     

顺序主成份分析--多元数据排序问题探讨

对于顺序变量,用最大方差的线性组合来定义主成份就会显得没有意义了.基于此,本文利用了所谓的顺序主成份分析(OPCA,它是主成份分析的一种典型扩展,可适用于顺序变量甚至虚拟变量),以我国35个主要城市的综合经济实力的排序为例,探讨了多元数据的排序问题.     

含无误差协变量的重复测量误差模型及其应用

文章讨论响应变量和部分协变量含测量误差的重复测量数据的建模和估计问题,获得参数极大似然估计的EM迭代算法以及估计量的渐近协方差矩阵,并利用Monte-Carlo模拟说明估计的有效性和模型的价值.最后,将研究理论用于处理气象数据的测量误差校正问题.     

Multinomial响应广义半参数回归模型及应用

在消费行为学领域经常碰到的离散选择数据就是Multinomial响应数据,此类数据通常采用Multinomial Logit线性回归模型来处理,不过如果回归变量中的一部分与对数机率向量间呈非线性关系,其余回归变量与对数机率向量间呈线性关系,就需要引入以对数机率向量为因变量的广义半参数回归模型来处理这类实际数据了.文章以一次手机用户生活形态调查数据为例,讨论了向量广义半参数回归模型在消费者行为研究中的应用.     

Heteroscedasticity and Distributional Assumptions in the Censored Regression Model

Data censoring causes ordinary least-square estimators of linear models to be biased and inconsistent. The Tobit estimator yields consistent estimators in the presence of data censoring if the errors are normally distributed. However, nonnormality or heteroscedasticity results in the Tobit estimators being inconsistent. Various estimators have been proposed for circumventing the normality assumption. Some of these estimators include censored least absolute deviations (CLAD), symmetrically censored least-square (SCLS), and partially adaptive estimators. CLAD and SCLS will be consistent in the presence of heteroscedasticity; however, SCLS performs poorly in the presence of asymmetric errors. This article extends the partially adaptive estimation approach to accommodate possible heteroscedasticity as well as nonnormality. A simulation study is used to investigate the estimators’ relative performance in these settings. The partially adaptive censored regression estimators have little efficiency loss for censored normal errors and appear to outperform the Tobit and semiparametric estimators for nonnormal error distributions and be less sensitive to the presence of heteroscedasticity. An empirical example is considered, which supports these results.     

Estimation for Location-Scale Models with Censored Data

This article considers a class of estimators for the location and scale parameters in the location-scale model based on ‘synthetic data’ when the observations are randomly censored on the right. The asymptotic normality of the estimators is established using counting process and martingale techniques when the censoring distribution is known and unknown, respectively. In the case when the censoring distribution is known, we show that the asymptotic variances of this class of estimators depend on the data transformation and have a lower bound which is not achievable by this class of estimators. However, in the case that the censoring distribution is unknown and estimated by the Kaplan–Meier estimator, this class of estimators has the same asymptotic variance and attains the lower bound for variance for the case of known censoring distribution. This is different from censored regression analysis, where asymptotic variances depend on the data transformation. Our method has three valuable advantages over the method of maximum likelihood estimation. First, our estimators are available in a closed form and do not require an iterative algorithm. Second, simulation studies show that our estimators being moment-based are comparable to maximum likelihood estimators and outperform them when sample size is small and censoring rate is high. Third, our estimators are more robust to model misspecification than maximum likelihood estimators. Therefore, our method can serve as a competitive alternative to the method of maximum likelihood in estimation for location-scale models with censored data. A numerical example is presented to illustrate the proposed method.     

Bias From Censored Regressors

We study the bias that arises from using censored regressors in estimation of linear models. We present results on bias in ordinary least aquares (OLS) regression estimators with exogenous censoring and in instrumental variable (IV) estimators when the censored regressor is endogenous. Bound censoring such as top-coding results in expansion bias, or effects that are too large. Independent censoring results in bias that varies with the estimation method—attenuation bias in OLS estimators and expansion bias in IV estimators. Severe biases can result when there are several regressors and when a 0–1 variable is used in place of a continuous regressor.     

Extending the family of Bayesian bootstraps and exchangeable urn schemes

A Bayesian bootstrap for a finite population with censored observations is introduced. It is shown to reduce to the finite population Bayesian bootstrap if there is no censoring and to reduce to the censored data Bayesian bootstrap for a large population. A class of general urn schemes for simulating exchangeable sequences of variables is introduced which is connected to the bootstrap method.     

Added variable plots for linear regression with censored data

In linear regression the structure of the hat matrix plays an important part in regression diagnostics. In this note we investigate the properties of the hat matrix for regression with censored responses in the presence of one or more explanatory variables observed without censoring. The censored points in the scatterplot are renovated to positions had they been observed without censoring in a renovation process based on Buckley-James censored regression estimators. This allows natural links to be established with the structure of ordinary least squares estimators. In particular, we show that the renovated hat matrix may be partitioned in a manner which assists in deciding whether further explanatory variables should be added to the linear model. The added variable plot for regression with censored data is developed as a diagnostic tool for this decision process.     

NONPARAMETRIC ESTIMATION FOR COMPETING RISKS

This paper considers the estimation of the ratio of two scale parameters when the data are censored. It emphasises characteristics of the asymptotic variance under censoring from a practical point of view. The estimator proposed by Padgett & Wei (1982) for the two-sample scale model is extended to the competing risks model. Asymptotic properties of the estimator are studied via its influence function. The use of influence functions permits a unified treatment of both models. Examples show and illustrate that under both models the variance can become infinite under some circumstances.     

A non-iterative Bayesian sampling algorithm for censored Student-t linear regression models

ABSTRACT

In this paper, we consider an effective Bayesian inference for censored Student-t linear regression model, which is a robust alternative to the usual censored Normal linear regression model. Based on the mixture representation of the Student-t distribution, we propose a non-iterative Bayesian sampling procedure to obtain independently and identically distributed samples approximately from the observed posterior distributions, which is different from the iterative Markov Chain Monte Carlo algorithm. We conduct model selection and influential analysis using the posterior samples to choose the best fitted model and to detect latent outliers. We illustrate the performance of the procedure through simulation studies, and finally, we apply the procedure to two real data sets, one is the insulation life data with right censoring and the other is the wage rates data with left censoring, and we get some interesting results.     

A large-scale monte carlo study of the buckley-james estimator with censored data

Estimation in the presence of censoring is an important problem. In the linear model, the Buckley-James method proceeds iteratively by estimating the censored values than re-estimating the regression coeffi- cients. A large-scale Monte Carlo simulation technique has been developed to test the performance of the Buckley-James (denoted B-J) estimator. One hundred and seventy two randomly generated data sets, each with three thousand replications, based on four failure distributions, four censoring patterns, three sample sizes and four censoring rates have been investigated, and the results are presented. It is found that, except for Type I1 censoring, the B-J estimator is essentially unbiased, even when the data sets with small sample sizes are subjected to a high censoring rate. The variance formula suggested by Buckley and James (1979) is shown to be sensitive to the failure distribution. If the censoring rate is kept constant along the covariate line, the sample variance of the estimator appears to be insensitive to the censoring pattern with a selected failure distribution. Oscillation of the convergence values associated with the B-J estimator is illustrated and thoroughly discussed.     

Student-t censored regression model: properties and inference

In statistical analysis, particularly in econometrics, it is usual to consider regression models where the dependent variable is censored (limited). In particular, a censoring scheme to the left of zero is considered here. In this article, an extension of the classical normal censored model is developed by considering independent disturbances with identical Student-t distribution. In the context of maximum likelihood estimation, an expression for the expected information matrix is provided, and an efficient EM-type algorithm for the estimation of the model parameters is developed. In order to know what type of variables affect the income of housewives, the results and methods are applied to a real data set. A brief review on the normal censored regression model or Tobit model is also presented.     

On the Bayesian inference of Kumaraswamy distributions based on censored samples

In this article we discuss Bayesian estimation of Kumaraswamy distributions based on three different types of censored samples. We obtain Bayes estimates of the model parameters using two different types of loss functions (LINEX and Quadratic) under each censoring scheme (left censoring, singly type-II censoring, and doubly type-II censoring) using Monte Carlo simulation study with posterior risk plots for each different choices of the model parameters. Also, detailed discussion regarding elicitation of the hyperparameters under the dependent prior setup is discussed. If one of the shape parameters is known then closed form expressions of the Bayes estimates corresponding to posterior risk under both the loss functions are available. To provide the efficacy of the proposed method, a simulation study is conducted and the performance of the estimation is quite interesting. For illustrative purpose, real-life data are considered.