Efficient estimation in semiparametric regression with possibly incomplete data

该奖项是根据2009年《美国复苏和再投资法案》(公法111-5)提供资金的。在缺失数据和半参数回归模型(即同时具有有限维和无限维参数的模型)的背景下，关于有效估计的工作很少，对于一般泛函的估计就更少了。大多数研究将他们的注意力局限于估计平均反应。相反，本研究项目研究的是对包含反应和协变量的任意预期的估计。调查员还将讨论密度和分布函数的估计问题。重点研究了响应随机缺失的半参数回归模型的有效估计。半参数模型的分析是一个具有实际意义的重要课题：在应用程序中，通常有一些关于可用数据结构的信息，但不足以指定适当的参数模型；半参数方法对这些信息进行了优化利用。然而，即使是简单的(广泛的)半参数模型，如部分线性模型，也还没有完全被理解。这项研究将加深我们对这一问题的理解。大多数预期结果也将适用于数据完整的情况。第一个研究链的目标是得出协变量和响应变量在半参数回归中的期望的有效估计值。第二部分重点研究了非线性回归模型中响应密度的估计。研究人员试图证明，对于某些表现良好的回归函数，响应密度可以用根n率来估计，并且，而且是有效的。预计用参数速率根n估计密度并不总是可能的：将调查限制和可能的替代方法。这两个方面的关键方法论创新是充分归因、效率和经验似然思想的结合。第三部分考虑了有缺失响应的非参数回归中误差分布函数的估计。许多科学研究都依赖于统计分析来得出结论。然而，在许多情况下，不完整的数据对这些结论的准确性构成了挑战。这适用于许多领域，包括流行病学、药物研究和涉及调查数据分析的社会/行为调查。这一研究项目的结果将使有缺失值的数据集得到更有效的处理，并提高关于数据的统计结论的准确性。尽管最近取得了重大进展，但效率低下的方法仍然经常使用。例如，按列表删除案例，以及不使用有关数据的所有可用信息的归罪方法。删除或忽略唯一或稀缺数据显然不是理想的选择。有效的分析将利用关于数据结构的所有可用信息，从而产生无偏见、分散度最小的估计方法：换句话说，更高的准确性。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). In the context of missing data and semiparametric regression models (i.e., models with both finite dimensional and infinite-dimensional parameters), little work has been done on efficient estimation and still less on estimating general functionals. Most studies limit their attention to estimating the mean response. In contrast, this research project studies estimation of arbitrary expectations involving response and covariables. The investigator will also address estimating densities and distribution functions. The focus is on efficient estimation in semiparametric regression with responses missing at random. The analysis of semiparametric models is an important topic with practical, real-world implications: in applications there is typically some information about the structure of the data available, but not sufficient to specify an appropriate parametric model; semiparametric methods make optimal use of that information. However, even simple (widespread) semiparametric models, such as the partly linear model, are not yet fully understood. This research will further our understanding. Most of the anticipated results will also apply to cases where data are complete. The first research strand has the goal of deriving efficient estimators of expectations of covariates and the response variable in semiparametric regression. A second strand focuses on estimation of the response density in the nonlinear regression model. The investigator intends to show that, for certain classes of well-behaved regression functions, the response density can be estimated with a root n rate and, moreover, efficiently. It is not anticipated that it will always be possible to estimate the density with the parametric rate root n: limitations and possible alternative approaches will be investigated. The key methodological innovation in these two strands is the combination of full imputation, efficiency and empirical likelihood ideas. The third strand considers estimation of the error distribution function in nonparametric regression with missing responses.Many scientific investigations depend upon statistical analysis to draw conclusions. In many cases, however, incomplete data present a challenge to the accuracy of those conclusions. This applies in many fields, including epidemiology, pharmaceutical research and social/behavioral investigations involving the analysis of survey data. The results of this research project will enable data sets with missing values to be treated more efficiently and improve the accuracy of statistical conclusions about the data. Despite significant recent progress, inefficient methods remain in frequent use. Examples include listwise deletion of cases, and imputation methods which do not use all the available information about the data. Deleting or disregarding unique or scarce data is clearly not a desirable option. Efficient analysis will make use of all available information about the structure of the data, leading to unbiased, least-dispersed estimation methods: in other words, greater accuracy.