Mathematical Sciences: Maximum Likelihood Methods in Complex Sample Surveys

9305573拟议研究旨在研究将最大似然推论应用于复杂调查数据的有效方法。我们打算采用的方法是基于加权分布的思想。它包括将样本中各单元的联合概率密度函数(Pdf)表示为样本包含概率(表示为观测数据的函数)和总体中保持的边际pdf的乘积。这些产品都是常态化的。ML估计器通过最大化所得到的相对于未知模型参数的加权pdf来获得。社会科学和政府机构经常使用调查数据来估计感兴趣的参数(例如，小区频率；变量之间的关系)。调查往往是复杂的，因为一个人是否在样本中的机会取决于许多因素。如统计学和计量经济学文献所述，在推断过程中不考虑抽样设计的特点可能会产生误导性的结果。拟议研究的意义在于，它有望为从复杂的调查数据中作出推论提供一种统一的方法，这些数据将解释抽样设计的已知特征。

9305573 The proposed research is to study efficient ways of applying maximum likelihood (ML) inference to complex survey data. The methodology we intend to apply is based on the ideas of weighted distributions. It consists of expressing the joint probability density functions (pdf) for units in the sample as products of the sample inclusion probabilities, expressed as functions of the observed data, and the marginal pdf holding in the population. These products are normalized. ML estimators are obtained by maximazing the resulting weighted pdf with respect to the unknown model parameters. Survey data are often used in the social sciences and by government agencies to estimate parameters of interest (e.g. cell frequencies; relationships among variables). Often the survey is complex in the sense that the chance that an individual is in the sample depends on many factors. As illustrated in the statistical and econometric literature, failure to account for the features of the sampling design in the inference process may yield misleading results. The significance of the proposed research is that it will hopefully provide a unified approach for drawing inferences from complex survey data that will account for the known features of the sampling design.