Bayesian nonparametric estimation of a copula

A copula can fully characterize the dependence of multiple variables. The purpose of this paper is to provide a Bayesian nonparametric approach to the estimation of a copula, and we do this by mixing over a class of parametric copulas. In particular, we show that any bivariate copula density can be arbitrarily accurately approximated by an infinite mixture of Gaussian copula density functions. The model can be estimated by Markov Chain Monte Carlo methods and the model is demonstrated on both simulated and real data sets.     

Designing stratified sampling in economic and business surveys

In most economic and business surveys, the target variables (e.g. turnover of enterprises, income of households, etc.) commonly resemble skewed distributions with many small and few large units. In such surveys, if a stratified sampling technique is used as a method of sampling and estimation, the convenient way of stratification such as the use of demographical variables (e.g. gender, socioeconomic class, geographical region, religion, ethnicity, etc.) or other natural criteria, which is widely practiced in economic surveys, may fail to form homogeneous strata and is not much useful in order to increase the precision of the estimates of variables of interest. In this paper, a stratified sampling design for economic surveys based on auxiliary information has been developed, which can be used for constructing optimum stratification and determining optimum sample allocation to maximize the precision in estimate.     

Marginal and Conditional Distribution Estimation from Double‐sampled Semi‐competing Risks Data

Informative dropout is a vexing problem for any biomedical study. Most existing statistical methods attempt to correct estimation bias related to this phenomenon by specifying unverifiable assumptions about the dropout mechanism. We consider a cohort study in Africa that uses an outreach programme to ascertain the vital status for dropout subjects. These data can be used to identify a number of relevant distributions. However, as only a subset of dropout subjects were followed, vital status ascertainment was incomplete. We use semi‐competing risk methods as our analysis framework to address this specific case where the terminal event is incompletely ascertained and consider various procedures for estimating the marginal distribution of dropout and the marginal and conditional distributions of survival. We also consider model selection and estimation efficiency in our setting. Performance of the proposed methods is demonstrated via simulations, asymptotic study and analysis of the study data.     

社会正义视域下碳排放权初始额度分配规则之选择

正义是碳排放权初始额度分配规则的首要德性。因此,碳排放权初始额度分配规则必须接受正当性之检验,使之符合社会正义的要求。我国正在推进碳排放权交易统一市场建设,碳排放权初始额度分配规则是其中一个关键要素。在此背景下,应当结合生态-社会-经济等多元目标,综合权衡,充分照顾欠发达地区、贫困人群生存与发展的需要,选择多元化的碳排放权交易初始配额分配规则,并建构有效的碳排放权初始额度抵扣机制,降低基本民生产品生产企业的成本。     

货币超额供给下的价格上涨

通过对我国货币的超额供给与价格水平上涨之间的关系的分析,可以看到在本轮通货膨胀过程中,资产市场价格早于商品市场价格的上涨,这是由于资本市场的储水池效应,减缓了货币供应量变化对商品价格变动的影响;在商品市场上,原材料能源价格由于需求拉动和国际能源价格的冲击而率先上涨,但由于货币超额供给所造成的低利率使得上游商品价格的上涨对下游商品价格的传递出现了障碍。     

Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed‐form Approximation Approach

When a continuous‐time diffusion is observed only at discrete dates, in most cases the transition distribution and hence the likelihood function of the observations is not explicitly computable. Using Hermite polynomials, I construct an explicit sequence of closed‐form functions and show that it converges to the true (but unknown) likelihood function. I document that the approximation is very accurate and prove that maximizing the sequence results in an estimator that converges to the true maximum likelihood estimator and shares its asymptotic properties. Monte Carlo evidence reveals that this method outperforms other approximation schemes in situations relevant for financial models.     

复杂抽样推断方法体系的比较研究

对复杂样本进行推断通常有两种体系,一种是传统的基于随机化理论的统计推断,另一种是基于模型的统计推断。传统的抽样理论以随机化理论为基础,将总体取值视为固定,随机性仅体现在样本的选取上,对总体的推断依赖于抽样设计。该方法在大样本情况下具有稳健估计量,但在小样本、数据缺失等情况下失效。基于模型的抽样推断认为总体是超总体模型中抽取的一个随机样本,对总体的推断取决于模型的建立,但在不可忽略抽样设计下估计量是有偏估计。在对这两类推断方法分析的基础上,提出抽样设计辅助的模型推断,并指出该方法在复杂抽样中具有重要的应用价值。     

Information on sexual behaviour when some data are missing

When tables contain missing values, statistical models that allow the non-response probability to be a function of the intended response have been proposed by several researchers. We investigate the properties of these methods in the context of a survey of the sexual behaviour of university students. Profile likelihoods can be computed, even when models are not identified and saturated profile likelihoods (making no assumptions about the non-response mechanism) are derived. Bayesian approaches are investigated and it is shown that their results may be highly sensitive to the prior specification. The proportion of responders answering 'yes' to the question 'have you ever had sexual intercourse?' was 73%. However, different assumptions about the non-responders gave proportions as low as 46% or as high as 83%. Our preferred estimate, derived from the response-saturated profile likelihood, is 67% with a 95% confidence interval of 58–74%. This is in line with other studies on response bias in the reports of young people's sexual behaviour that suggest that the respondents overrepresent the sexually active.