Efficient Estimation in Semiparametric Models

这位主要研究者建议继续他在半参数模型中有效估计的研究计划，重点放在非参数和半参数回归模型、部分知道边际的双变量模型和时间序列模型上。特别关注具有独立创新的时间序列模型中曲线(如平稳密度和条件期望)的(有效)n根相容估计的可能性。回归模型的研究将集中在随机缺失的诊断和估计上。关于后者，将研究完全推定估计器。这种估计器不仅对缺失的响应进行推定，而且还对观察到的响应进行推定。目前，主要调查者的工作表明，完全推定的估计器通常比部分推定的估计器更好，后者只推算丢失的响应。这项研究的一个目标是证明这一猜想，并证明完全推定的估计器甚至可以是有效的。关于双变量模型的工作将处理迄今获得的已知和相等边际的微调结果，并将这种结果扩展到更一般的模型，包括通过参数将边际分布联系在一起的模型。此外，还计划撰写两部专著，一部是关于回归模型的有效估计，另一部是关于时间序列模型的有效估计，这将推动半参数模型的有效估计理论的发展，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学的领域中广泛存在，因此本文的研究将对所有这些领域产生影响。例如，关于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中有应用；关于双变量模型的结果在精算科学和医学研究中有应用；关于推算的结果在医学研究中很有用。计划出版的专著旨在将拟议研究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.