Imputation Methodology for Complex Survey Problems

本文的研究重点是对无响应的调查数据进行归算和归算后方差估计。为了估计人口总数和分位数，将研究边际归算（如随机热甲板归算、最近邻归算和随机回归归算）。研究者还将研究联合归算（用于估计相关系数或列联表中的单元概率等参数）和不可忽略响应下的归算。对于每种输入方法，将使用直接推导方法或复制方法（如jackknife，平衡半样本和bootstrap）研究考虑非响应和输入的方差估计。许多统计机构和政府机构通过调查收集数据。大多数调查都没有回应。部分抽样单位在调查中予以配合，但未对某些问题作出回答，即为项目不答复。为无应答者插入值的Imputation技术是对项目无应答的常用补偿程序。在某些情况下，如果适当地使用辅助信息，则可增加统计的准确性。对估算方法的一个基本要求是，通过将估算值视为观测数据，并使用为无响应情况设计的标准估算公式，可以获得无偏（或近似无偏）的调查估计量。这就需要发展归责方法和统计分析程序，以考虑到无反应和归责。由于大部分的研究课题都是由人口普查局（Census Bureau）、劳工统计局（Bureau of Labor Statistics）、西部统计局（Westat）和加拿大统计局（Statistics Canada）等调查机构存在的问题所驱动的，因此研究结果将对这些调查机构的归算和方差估计方法产生重大影响。

The proposed research focuses on imputation and variance estimation after imputation for survey data with nonresponse. Marginal imputation (such as random hot deck imputation, nearest neighbor imputation, and random regression imputation) will be studied for the purpose of estimating population totals and quantiles. The investigator will also study joint imputation (for estimating parameters such as the coefficients of correlation or the cell probabilities in a contingency table) and imputation under nonignorable response. For each imputation method, variance estimation that takes nonresponse and imputation into account will be studied, using a direct derivation approach or a replication method such as the jackknife, the balanced half samples, and the bootstrap.Many statistics and government agencies collect data through surveys. Most surveys have nonresponse. Item nonresponse occurs when some sampled units cooperate in the survey but fail to provide answers to some questions. Imputation techniques, which insert values for nonrespondents, are commonly used compensation procedures for item nonresponse. In some cases, when auxiliary information is properly used, imputation increases statistical accuracy. An essential requirement for an imputation method is that one can obtain unbiased (or approximately unbiased) survey estimators by treating the imputed values as observed data and using the standard estimation formulas designed for the case of no nonresponse. This requires developments on imputation methodology and statistical analysis procedures to take nonresponse and imputation into account. Since most of the proposed research topics are motivated by problems in survey agencies such as the Census Bureau, the Bureau of Labor Statistics, Westat, and Statistics Canada, results obtained from the proposed research will have significant impacts on the imputation and variance estimation methodology for these survey agencies.