Efficient Estimation in Semiparametric Models

首席研究员建议继续他在半参数模型中的有效估计的研究计划，重点是非参数和半参数回归模型，关于边际部分知识的二元模型，以及时间序列模型。我们将特别关注具有独立创新的时间序列模型中平稳密度和条件期望等曲线的（有效的）根n一致估计的可能性。回归模型的工作将集中于诊断和在随机丢失响应时的归因。关于后者，将研究完全估算的估计量。这样的估计器不仅可以估计缺失的响应，还可以估计观察到的响应。目前主要研究者的工作表明，完全估计量通常比部分估计量更好，部分估计量只估算缺失的响应。研究的一个目标是证明这一猜想，并表明完全估算的估计器甚至可以是有效的。关于二元模型的工作将处理到目前为止已知的和相等的边际的微调结果，并将这些结果扩展到更一般的模型，包括那些边际分布通过参数联系起来的模型。还计划撰写两本专著，一本是关于回归模型的有效估计，另一本是关于时间序列模型的有效估计。所提出的研究将推进半参数模型的有效估计理论，并将为许多具体问题的数据分析提供更有效的方法。由于半参数模型在许多使用统计的领域中广泛存在，因此所提出的研究将对所有这些领域产生影响。例如，时间序列和马尔可夫链模型的结果在计量经济学和数学金融学中有应用；双变量模型的结果在精算科学和医学研究中有应用；推断结果在医学研究中是有用的。计划的专著旨在将拟议研究中的一些研究传播给更广泛的受众。

The Principle Investigator proposes to continue his research program on efficient estimation in semiparametric models with an emphasis on non- and semiparametric regression models, on bivariate models with partial knowledge about the marginals, and on time series models.Special attention will be paid to the possibility of (efficient) root-n consistent estimation of curves such as stationary densities and conditional expectations in time series models with independent innovations. Work on regression models will focus on diagnostics and on imputing when responses are missing at random.In connection with the latter fully imputed estimators will be studied.Such estimators impute not only the missing but also the observed responses.Current work by the Principal Investigator suggests that the fully imputed estimator is typically better than the partly imputed estimator, which only imputes the missing responses. One goal of the research is to prove this conjecture and to show that fully imputed estimators can even be made to be efficient. The work on bivariate models will deal with fine-tuning results for known and equal marginals obtained so far,and on extending such results to more general models including those in which the marginal distributions are linked through a parameter. Work on two monographs, one on efficient estimation in regression modelsand the other on efficient estimation in time series models, is also planned.The proposed research will advance the theory of efficient estimation in semiparametric models and will provide more efficient ways of analyzing data in many concrete problems. Since semiparametric models are widespread in many fields that use statistics, the proposed research will have an impact on all these fields. For example, results on time series and Markov chain models have applications in econometrics and mathematical finance; results on bivariate models have applications in actuarial sciences and in medical research; results on imputing are useful in medical studies.The planned monographs are intended to disseminate some of the research from the proposed research to a wider audience.