Partial identification in the statistical matching problem
研究了多个数据集整合时因变量未共同观测导致的模型不可识别问题，提出一种吉布斯采样方法，通过协方差矩阵的正定补全来界定参数可行域，适用于高维统计匹配。
The statistical matching problem involves the integration of multiple datasets where some variables are not observed jointly. This missing data pattern leaves most statistical models unidentifiable. Statistical inference is still possible when operating under the framework of partially identified models, where the goal is to bound the parameters rather than to estimate them precisely. In many matching problems, developing feasible bounds on the parameters is equivalent to finding the set of positive-definite completions of a partially specified covariance matrix. Existing methods for characterising the set of possible completions do not extend to high-dimensional problems. A Gibbs sampler to draw from the set of possible completions is proposed. The variation in the observed samples gives an estimate of the feasible region of the parameters. The Gibbs sampler extends easily to high-dimensional statistical matching problems.