基于C-K模型及其改进的高高龄人口死亡率模型研究

目前,国际上关于高龄人口死亡率估计的方法主要包括经典的参数模型估计方法,如用Gompertz分布、Makeham分布拟合高龄人口的死亡率。文章将着重探究Coale-Kisker模型在高高龄人口死亡率拟合中的应用,并针对高高龄人口死亡数据足够多时,对经典的Coale-Kisker模型提出适当的改进。     

我国人口死亡风险异质与混合模型研究

多人口随机死亡率模型是人口统计和保险精算领域的前沿问题。建立符合我国人口特征的死亡率预测模型，对人口预测、长寿风险度量和积极管理长寿风险具有重要意义。然而，当前研究中对人口死亡风险异质性问题的关注较少，不能为多人口随机死亡率建模提供科学的研究假设。本文从我国人口死亡风险异质性的检验出发，构建两性别人口死亡率联合预测的混合泊松公因子模型，并给出极大似然参数估计的迭代算法，对我国男女两性别人口死亡率进行联合建模和预测，最后用于对保险公司养老年金的长寿风险资本需求测算。研究表明，混合泊松公因子模型能够有效刻画人口死亡风险的异质性，提升模型拟合优度，有效避免传统模型低估人口死亡率改善的弊端，并且死亡率性别比变动趋势符合人类生物规律。在风险导向的第二代偿付能力体系下，本文提出的死亡率模型能够为保险公司提供更稳健的长寿风险资本评估。     

空间误差分量模型的Bootstrap LM检验

空间误差分量模型(Spatial Error Components,SEC)传统的空间相关性LM检验存在严重的水平扭曲和较低的检验功效,导致检验统计量失效.文章将Bootstrap方法应用于SEC模型的空间相关性LM检验,提高检验统计量的有效性.Monte Carlo模拟实验表明,Bootstrap LM检验的水平受误差项分布、空间权重矩阵和样本量影响较小,并且远优于渐近LM检验,具有理想的检验水平;渐近LM检验和Bootstrap LM检验的功效均随着空间相关性的增强,及样本量的增大而增大,但Bootstrap LM检验在各种情形下均具有更高的检验功效,尤其是样本量较小时.简言之,Bootstrap LM检验是SEC模型更为优越的空间相关性检验方法.     

我国男女两性老龄人口死亡率联合建模与预测

老龄人口死亡率建模和预测是长寿风险度量和养老金风险管理的基础。在我国,退休年龄及以上老龄人口死亡数据稀少,随机波动大,构建能够捕捉老龄人口死亡率随性别、年龄和时间变动的动态预测模型成为难题。本文采用Logistic两人口死亡率模型研究我国老龄人口死亡率的建模与预测。首先,运用死亡率数据质量较好的我国台湾地区数据,对模型结构进行选择,并检验模型的稳健性和预测性能。其次,基于我国大陆地区死亡率数据对模型结构进行二次验证和选择,应用所选模型对大 陆地区老龄死亡率进行建模和预测。结果显示,对于我国男女老龄死亡率的拟合和预测,Logistic 两人口模型均优于单人口CBD模型。最后,运用Logistic两人口死亡率模型对死亡率在年龄和时间两个维度上外推和预测,计算出时期和队列老龄人口分年龄的预期余寿,为养老金精算评估和长寿风险分析提供更准确的数据支持。     

线性回归模型Bootstrap LM-Lag检验有效性研究

基于OLS估计残差,将Bootstrap方法用于空间滞后相关LM-Lag检验。在不同的误差结构和空间权重矩阵条件下,比较Bootstrap LM-Lag检验和渐近检验的水平扭曲和功效。通过Monte Carlo实验表明,当误差项不服从经典正态分布假设时,LM-Lag渐近检验存在严重的水平扭曲,Bootstrap检验能够有效地校正水平扭曲,并且Bootstrap LM-Lag检验的功效与渐近检验近似;无论误差项是否服从正态分布,从水平扭曲和功效角度看,线性回归模型Bootstrap LM-Lag检验有效。     

基于长寿背景下的企业年金风险评估

在死亡率不断降低,预期寿命不断提高的背景下,企业年金实现一定替代率目标的难度不断增大,面临的长寿风险越来越不容忽视。在中国人口死亡率最优模型基础上,通过企业年金比率模型评估了三种不同年龄结构企业年金的长寿风险,并在基于Bootstrap方法的VAR模型上考虑了投资风险,对企业年金进行综合风险分析。结果表明,当其他风险都能被完全对冲时,未来死亡率降低及预期寿命延长会对企业年金实现目标养老待遇产生较大影响,并且评估期越长,企业年金积累的长寿风险越大。     

考虑死亡率组内差异的Lee-Carter模型的改进与应用

文章在经典Lee-Carter模型的基础上,将各个时间、年龄组内的死亡率差异考虑入模型的构建中,提出死亡人口服从负二项分布的Lee-Carter模型改进形式,并运用中国1993～2009年分年龄分性别的死亡率对模型进行了量化分析。分析表明,改进后的模型优于经典泊松分布假设下的模型。模型残差图显示中国人口死亡现象没有队列效应。最后,本文运用改进后模型预测出未来6年内中国分性别分年龄的死亡率。     

空间经济计量滞后模型Bootstrap Moran检验功效的模拟分析

 当误差项不服从独立同分布时,利用Moran’s I统计量的渐近检验,无法有效判断空间经济计量滞后模型2SLS估计残差间存在空间关系与否。本文采用两种基于残差的Bootstrap方法,诊断空间经济计量滞后模型残差中的空间相关关系。大量Monte Carlo模拟结果显示,从功效角度看,无论误差项服从独立同分布与否,与渐近检验相比,Bootstrap Moran检验都具有更好的有限样本性质,能够更有效地进行空间相关性检验。尤其是,在样本量较小和空间衔接密度较高情况下,Bootstrap Moran检验的功效显著大于渐近检验。     

基于均衡关系的中国人口死亡率预测模型

人口死亡率反映了人口的死亡程度,准确预测死亡率是人口科学及人口经济学研究的重点之一,同时也是长寿风险测量的重要数据基础。基于Lee-Carter模型,探索中国大陆与台湾地区死亡率的相关性,通过协整分析考虑两地死亡率的长期均衡关系,创新性地建立基于相关性的向量误差修正模型(VECM),克服传统自回归移动平均模型(ARIMA)使用有限数据进行预测的局限性;均方预测误差作为检验标准,结果表明:基于VECM模型的预测效果比传统的预测效果更佳;基于中国大陆地区和台湾地区的死亡率长期均衡关系,可以为两地联合长寿债券的定价提供重要参考。     

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。     

Reference priors for constrained rate models of count data

We derive reference priors for constrained rate models of count data using the sequential algorithm of Berger and Bernardo (1992b). The event counts for various groups of subjects are modeled as discrete random variables (Poisson, binomial, or negative binomial) with group specific rates. We consider situations in which the groups can be completely ordered according to one covariate. The priors enforce monotonicity (or monotonicity and convexity) of the rates with respect to the ordering. We use the priors to model a data set on mortality rates for men in different age groups assuming that the mortality rates increase with respect to age. We also consider the situation in which the parameter space is augmented to include rates corresponding to unobserved age groups, and the case of a random upper bound on the mortality rates. In addition, we provide an evaluation of the out-of-sample predictive performance of the proposed methods.     

Weighted-bootstrap alignment of explanatory variables

Adjustment for covariates is a time-honored tool in statistical analysis and is often implemented by including the covariates that one intends to adjust as additional predictors in a model. This adjustment often does not work well when the underlying model is misspecified. We consider here the situation where we compare a response between two groups. This response may depend on a covariate for which the distribution differs between the two groups one intends to compare. This creates the potential that observed differences are due to differences in covariate levels rather than “genuine” population differences that cannot be explained by covariate differences. We propose a bootstrap-based adjustment method. Bootstrap weights are constructed with the aim of aligning bootstrap–weighted empirical distributions of the covariate between the two groups. Generally, the proposed weighted-bootstrap algorithm can be used to align or match the values of an explanatory variable as closely as desired to those of a given target distribution. We illustrate the proposed bootstrap adjustment method in simulations and in the analysis of data on the fecundity of historical cohorts of French-Canadian women.     

THE USE OF AGGREGATE DATA TO ESTIMATE GOMPERTZ‐TYPE OLD‐AGE MORTALITY IN HETEROGENEOUS POPULATIONS

We consider two related aspects of the study of old‐age mortality. One is the estimation of a parameterized hazard function from grouped data, and the other is its possible deceleration at extreme old age owing to heterogeneity described by a mixture of distinct sub‐populations. The first is treated by half of a logistic transform, which is known to be free of discretization bias at older ages, and also preserves the increasing slope of the log hazard in the Gompertz case. It is assumed that data are available in the form published by official statistical agencies, that is, as aggregated frequencies in discrete time. Local polynomial modelling and weighted least squares are applied to cause‐of‐death mortality counts. The second, related, problem is to discover what conditions are necessary for population mortality to exhibit deceleration for a mixture of Gompertz sub‐populations. The general problem remains open but, in the case of three groups, we demonstrate that heterogeneity may be such that it is possible for a population to show decelerating mortality and then return to a Gompertz‐like increase at a later age. This implies that there are situations, depending on the extent of heterogeneity, in which there is at least one age interval in which the hazard function decreases before increasing again.     

基于贝叶斯的Bootstrap置信区间

在许多领域中,Bootstrap成为一种数据处理的有效方法。很多情况下,模型中感兴趣的参数的置信区间难以构建,为了解决这一问题,文章提出了一个新的贝叶斯Bootstrap置信区间的估计量,并做了蒙特卡洛模拟比较,结果比经典区间估计方法和经典Bootstrap方法更优,并进行了实例分析。     

The long-term pattern of adult mortality and the highest attained age

Recent new data on old age mortality point to a particular model for the way in which the probability of dying increases with age. The model is found to fit not only modern data but also some widely spaced historical data for the 19th and 17th centuries, and even some estimates for the early mediaeval period. The results show a pattern which calls for explanation. The model can also be used to predict a probability distribution for the highest age which will be attained in given circumstances. The results are relevant to the current debate about whether there is a fixed upper limit to the length of human life.     

Modeling heteroscedastic age-period-cohort cancer data

The extent to which cancer will be a burden on the Canadian health-care system will be determined by future cancer rates and future population levels in the high-risk age groups. Parametric models of incidence and mortality rates for various cancers may be used to obtain medium-term forecasts of rates, which then can be used in conjunction with population projections to obtain forecasts of total incidence and mortality. Age-period-cohort cancer data often exhibit marked heteroscedasticity, which complicates the modeling of the data. Methods to allow for the effects of this heteroscedasticity on residual processes are developed and discussed in the context of modeling Canadian female breast-cancer incidence data.     

A new class of mixture models for differential gene expression in DNA microarray data

One of the fundamental issues in analyzing microarray data is to determine which genes are expressed and which ones are not for a given group of subjects. In datasets where many genes are expressed and many are not expressed (i.e., underexpressed), a bimodal distribution for the gene expression levels often results, where one mode of the distribution represents the expressed genes and the other mode represents the underexpressed genes. To model this bimodality, we propose a new class of mixture models that utilize a random threshold value for accommodating bimodality in the gene expression distribution. Theoretical properties of the proposed model are carefully examined. We use this new model to examine the problem of differential gene expression between two groups of subjects, develop prior distributions, and derive a new criterion for determining which genes are differentially expressed between the two groups. Prior elicitation is carried out using empirical Bayes methodology in order to estimate the threshold value as well as elicit the hyperparameters for the two component mixture model. The new gene selection criterion is demonstrated via several simulations to have excellent false positive rate and false negative rate properties. A gastric cancer dataset is used to motivate and illustrate the proposed methodology.     

The future of old-age security in the Federal Republic of Germany

The future aspects of old age security in the Federal Republic of Germany are considered primarily according to the criteria of demographic changes to be expected or presumed. The starting point of our simulations is a strongly declining birth rate which effects a drop in the population growth as well as different criteria concerning the age structure. It is shown that, apart from the demographic structure, the economic development is of decisive importance for old age security. By a model variant obtained by a broad spectrum of simulations, it is shown that an increase in the standard of living affecting all population groups (including pensioners) can be attained provided that the manpower potential is well utilized and the labor productivity is progressing satisfactorily. However, by no means can problems concerning strategies of distribution that are likely to appear be solved by a complete denial of the financing procedure by persons currently employed. The social security of the older persons who no longer are gainfully employed can be financed by the current national product. (author's)