Multiple Imputation of Missing or Faulty Values Under Linear Constraints
提出一种贝叶斯联合模型，在满足线性约束（如变量边界、比率或和的不等式）的条件下，对缺失或错误值进行插补，使用狄利克雷过程混合多元正态分布处理复杂分布特征，并通过Hit-and-Run采样保证插补值满足约束。
Many statistical agencies, survey organizations, and research centers collect data that suffer from item nonresponse and erroneous or inconsistent values. These data may be required to satisfy linear constraints, for example, bounds on individual variables and inequalities for ratios or sums of variables. Often these constraints are designed to identify faulty values, which then are blanked and imputed. The data also may exhibit complex distributional features, including nonlinear relationships and highly nonnormal distributions. We present a fully Bayesian, joint model for modeling or imputing data with missing/blanked values under linear constraints that (i) automatically incorporates the constraints in inferences and imputations, and (ii) uses a flexible Dirichlet process mixture of multivariate normal distributions to reflect complex distributional features. Our strategy for estimation is to augment the observed data with draws from a hypothetical population in which the constraints are not present, thereby taking advantage of computationally expedient methods for fitting mixture models. Missing/blanked items are sampled from their posterior distribution using the Hit-and-Run sampler, which guarantees that all imputations satisfy the constraints. We illustrate the approach using manufacturing data from Colombia, examining the potential to preserve joint distributions and a regression from the plant productivity literature. Supplementary materials for this article are available online.