Marginal Likelihood Estimation with the Cross-Entropy Method

We consider an adaptive importance sampling approach to estimating the marginal likelihood, a quantity that is fundamental in Bayesian model comparison and Bayesian model averaging. This approach is motivated by the difficulty of obtaining an accurate estimate through existing algorithms that use Markov chain Monte Carlo (MCMC) draws, where the draws are typically costly to obtain and highly correlated in high-dimensional settings. In contrast, we use the cross-entropy (CE) method, a versatile adaptive Monte Carlo algorithm originally developed for rare-event simulation. The main advantage of the importance sampling approach is that random samples can be obtained from some convenient density with little additional costs. As we are generating independent draws instead of correlated MCMC draws, the increase in simulation effort is much smaller should one wish to reduce the numerical standard error of the estimator. Moreover, the importance density derived via the CE method is grounded in information theory, and therefore, is in a well-defined sense optimal. We demonstrate the utility of the proposed approach by two empirical applications involving women's labor market participation and U.S. macroeconomic time series. In both applications, the proposed CE method compares favorably to existing estimators.     

基于主成分和支持向量机模型在人口预测中的应用

人口问题是一个复杂、受诸多因素影响的社会问题,准确地预测人口数量对于制定国民经济计划和社会发展战略有着深远的意义。针对神经网络预测算法易陷入局部极小、输入数据具有较强相关性的问题,建立了一种基于主元分析(PCA)与支持向量机(SVM)相结合的人口预测模型,并对我国人口总量进行预测。结果表明,该模型比单变量GM(1,1)和BP神经网络模型预测精度有了明显提高。     

FDI对产业结构调整的影响

基于东北三省2006—2016年动态面板数据,建立固定效应模型和面板VAR模型,利用Stata软件引入人力资本变量,实证分析三省FDI对产业结构调整的影响。研究结果表明:东北三省FDI变量对产业结构变量影响减弱,且有负面影响趋势。由于FDI变量使用的是相对值,实证结果不能说明其对产业结构调整存在负面影响,但说明了FDI对产业结构调整的作用在弱化。引入人力资本作为技术进步的代理变量,实证分析得出人力资本对产业结构存在正向作用的结论,说明人力资本显著促进了产业结构调整。     

An Additive Genetic Gamma Frailty Model for Linkage Analysis of Diseases with Variable Age of Onset Using Nuclear Families

Many late-onset complex diseases exhibit variable age of onset. Efficiently incorporating age of onset information into linkage analysis can potentially increase the power of dissecting complex diseases. In this paper, we treat age of onset as a genetic trait with censored observations. We use multiple markers to infer the inheritance vector at the disease susceptibility (DS) locus in order to extract information about the inheritance pattern of the disease allele in a pedigree. Given the inheritance distribution at the DS locus, we define the genetic frailty for each individual within a nuclear family as the sum of frailties due to a putative major disease gene and a polygenic effect due to any remaining DS loci. Conditioning on these frailties we use the proportional hazards model for the risk of developing disease. We show that a test of linkage can be formulated as a test of zero variance due to a specific locus of the additive gamma frailties. Maximum likelihood estimation, using the EM algorithm, and likelihood ratio tests are employed for parameter estimation and tests of linkage. A simulation study presented indicates that the proposed method is well behaved and can be more powerful than the currently available allele-sharing based linkage methods. A breast cancer data example is used for illustration.     

Characterization of an optimal matrix estimator under convex loss function

Characterization of an optimal vector estimator and an optimal matrix estimator are obtained. In each case appropriate convex loss functions are considered. The results are illustrated through the problems of simultaneous unbiased estimation, simultaneous equivariant estimation and simultaneous unbiased prediction. Further an optimality criterion is proposed for matrix unbiased estimation and it is shown that the matrix unbiased estimation of a matrix parametric function and the minimum variance unbiased estimation of its components are equivalent.     

An approach to model complex high–dimensional insurance data

Summary: This paper describes common features in data sets from motor vehicle insurance companies and proposes a general approach which exploits knowledge of such features in order to model high–dimensional data sets with a complex dependency structure. The results of the approach can be a basis to develop insurance tariffs. The approach is applied to a collection of data sets from several motor vehicle insurance companies. As an example, we use a nonparametric approach based on a combination of two methods from modern statistical machine learning, i.e. kernel logistic regression and -support vector regression.*This work was supported by the Deutsche Forschungsgemeinschaft (SFB 475, Reduction of complexity in multivariate data structures) and by the Forschungsband Do-MuS from the University of Dortmund. I am grateful to Mr. A. Wolfstein and Dr. W. Terbeck from the Verband öffentlicher Versicherer in Düsseldorf, Germany, for making available the data set and for many helpful discussions.     

Likelihood Ratio Tests for High‐Dimensional Normal Distributions

In their recent work, Jiang and Yang studied six classical Likelihood Ratio Test statistics under high‐dimensional setting. Assuming that a random sample of size n is observed from a p‐dimensional normal population, they derive the central limit theorems (CLTs) when p and n are proportional to each other, which are different from the classical chi‐square limits as n goes to infinity, while p remains fixed. In this paper, by developing a new tool, we prove that the mentioned six CLTs hold in a more applicable setting: p goes to infinity, and p can be very close to n. This is an almost sufficient and necessary condition for the CLTs. Simulations of histograms, comparisons on sizes and powers with those in the classical chi‐square approximations and discussions are presented afterwards.     

国际油价冲击对中国对外贸易影响的实证分析

为研究国际油价冲击和美国、日本等国家进出口贸易量的波动对中国进出口贸易的影响,选取与中国贸易往来较多的18个国家和地区,包括欧元区主要国家、金砖国家及东盟地区国家,构建全局向量自回归模型,借助脉冲响应函数,分析国际油价及他国进出口贸易量对中国国际贸易的影响方向和程度。研究认为,国际油价波动对中国进出口贸易额均有影响,油价上涨对中国进口产生一定程度的正向效应,对中国出口产生一定程度的负向效应;美国、日本进口增加会对中国进出口贸易产生显著的负效应,相反,美国、日本出口增加会对中国进出口贸易产生显著的正效应,并且两者都对中国进口贸易抑制作用显著;中国外贸对贸易伙伴国进出口贸易波动的反应比对油价波动的反应更加显著。因此,国际油价上涨在一定程度上会促进中国进口,阻碍中国出口;美国、日本两国进出口贸易对中国对外贸易影响显著,美国、日本进出口冲击均对中国进口贸易更具影响力,但是相较于美国、日本外贸冲击,国际油价对中国国际贸易影响较小。     

山东省农业经济增长影响因素动态分析

运用1980~2009年山东省农业经济的相关数据,通过建立山东省第一产业GDP,第一产业就业人数,农作物播种总面积以及财政支农支出四变量的无约束向量自回归模型（VAR）以及向量误差修正模型（VEC）,对影响农业经济增长的因素进行了动态分析,进而探讨了山东省农业经济增长的长期趋势。结果表明,第一产业就业人数以及财政支农支出对山东省农业经济的增长有重要的影响,在此结论的基础上,提出相应的政策建议。