半参数变系数回归模型的空间相关性检验

对半参数变系数回归模型,构造了新的空间相关性检验统计量,利用三阶矩 逼近方法导出了其检验 值的近似计算公式,蒙特卡罗模拟结果表明该统计量在检测空间相关性方面具有较高的准确性和可靠性。同时考察了误差项服从不同分布时的检验功效,体现出该检验方法的稳健性。进一步,我们还给出了检验统计量的Bootstrap方法以及检验水平的模拟效果。     

Method of Moments Estimation in Linear Regression with Errors in both Variables

Recently, in this journal, there has been revised attention on estimating the parameters of the errors in variables, linear structural model. For example, O’Driscoll and Ramirez (2011) used a geometric approach to give insight into the performance of various slope estimators for the linear structural model as introduced by the present author. This article aims to provide a unified method of moments approach for estimating the parameters in the linear structural model, concentrating attention on estimators using the higher moments, which to date has received only little attention in the literature.     

Simulation/Regression Pricing Schemes for CVA Computations on CDO Tranches

We devise simulation/regression numerical schemes for pricing the CVA on CDO tranches, where CVA stands for Credit Valuation Adjustment, or price correction accounting for the defaultability of a counterparty in an OTC derivatives transaction. This is done in the setup of a continuous-time Markov chain model of default times, in which dependence between credit names is represented by the possibility of simultaneous defaults. The main idea of this article is to perform the nonlinear regressions which are used for computing conditional expectations, in the time variable for a given state of the model, rather than in the space variables at a given time in diffusive setups. This idea is formalized as a lemma which is valid in any continuous-time Markov chain model. It is then implemented on the targeted application of CVA computations on CDO tranches.     

非线性参数异质Phillips曲线模型及应用

基于分位数回归理论与非线性回归方法,提出一个包容性较强的模型：非线性参数异质Phillips曲线模型,并给出其估计、检验与条件密度预测方法。该模型不仅可用于刻画Phillips曲线的非线性与非对称等典型特征,而且还可以揭示在不同经济环境下通货膨胀的完整分布变动规律,从而能够准确掌握通货膨胀的不确定性,便于科学决策。最后,将该模型应用于中国Phillips曲线特征研究,结果显示：该模型在拟合优度、结构分析、预测能力等方面优于其他Phillips曲线模型。     

一类基于非参数回归的条件异方差检验

现有基于参数模型构造的条件异方差检验往往存在模型设定偏误问题。为了避免模型误设对检验结果的影响,并且同时捕获多种条件异方差现象,本文基于非参数回归构造了不依赖于特定模型形式的条件异方差检验统计量。该统计量可视作条件方差和无条件方差之间差异的加权平均,在原假设成立时渐近服从标准正态分布。数值模拟结果一方面表明本文统计量具有良好的有限样本性质,另一方面也说明条件均值模型误设会导致错误地拒绝条件同方差的原假设,凸显了本文引入非参数方法构造条件异方差检验的必要性。实证分析采用本文统计量探讨了国际主要股指收益率的条件异方差现象,得到了与Engle (1982)不同的检验结果,可能意味着股指收益率呈现出非线性动态特征。     

Bootstrap adjustments of signed scoring rule root statistics

Scoring rules give rise to methods for statistical inference and are useful tools to achieve robustness or reduce computations. Scoring rule inference is generally performed through first-order approximations to the distribution of the scoring rule estimator or of the ratio-type statistic. In order to improve the accuracy of first-order methods even in simple models, we propose bootstrap adjustments of signed scoring rule root statistics for a scalar parameter of interest in presence of nuisance parameters. The method relies on the parametric bootstrap approach that avoids onerous calculations specific of analytical adjustments. Numerical examples illustrate the accuracy of the proposed method.     

An evaluation of the bootstrap for model validation in mixture models

Bootstrapping has been used as a diagnostic tool for validating model results for a wide array of statistical models. Here we evaluate the use of the non-parametric bootstrap for model validation in mixture models. We show that the bootstrap is problematic for validating the results of class enumeration and demonstrating the stability of parameter estimates in both finite mixture and regression mixture models. In only 44% of simulations did bootstrapping detect the correct number of classes in at least 90% of the bootstrap samples for a finite mixture model without any model violations. For regression mixture models and cases with violated model assumptions, the performance was even worse. Consequently, we cannot recommend the non-parametric bootstrap for validating mixture models.

The cause of the problem is that when resampling is used influential individual observations have a high likelihood of being sampled many times. The presence of multiple replications of even moderately extreme observations is shown to lead to additional latent classes being extracted. To verify that these replications cause the problems we show that leave-k-out cross-validation where sub-samples taken without replacement does not suffer from the same problem.     

A note on multivariate linear regression

In this note, a hypothesis test based on relevant statistical differences is proposed for multivariate linear regression models whose design matrix rank does not equal the number of regression variables. A statistical example is also provided to illustrate the proposed hypothesis test.     

基于多源数据融合的个人信用评分研究

随着信息技术的发展,数据来源越来越多,一方面可以更加精准、科学地刻画个人信用状况,但另一方面,由于数据来源多、结构复杂等问题,对传统的征信技术带来了挑战。本文提出了基于多源数据融合的个人信用模型,可以同时对多个数据集进行建模和变量选择,同时考虑了数据集间的相似性和异质性。通过模拟实验发现,本文所提出的整合模型在变量选择和分类效果方面都具有明显的优势。最后,将整合模型应用于城市和农村两个数据集的个人信用评分中。