This article introduces a new instrumental variable approach for estimating unknown population parameters with data having nonrandom missing values. With coarse and discrete instruments, Shao and Wang (2016) proposed a semiparametric method that uses the added information to identify the tilting parameter from the missing data propensity model. A naive application of this idea to continuous instruments through arbitrary discretizations is apt to be inefficient, and maybe questionable in some settings. We propose a nonparametric method not requiring arbitrary discretizations but involves scanning over continuous dichotomizations of the instrument; and combining scan statistics to estimate the unknown parameters via weighted integration. We establish the asymptotic normality of the proposed integrated estimator and that of the underlying scan processes uniformly across the instrument sample space. Simulation studies and the analysis of a real data set demonstrate the gains of the methodology over procedures that rely either on arbitrary discretizations or moments of the instrument.
翻译:本条引入了一种新的工具变量方法,用非随机缺失值的数据来估计未知人口参数。用粗糙和离散的仪器,Shao和Wang(Wang)提出了一种半参数方法,利用所增加的信息从缺失的数据偏向模型中确定倾斜参数。通过任意离散对连续仪器天真地应用这一想法可能效率不高,在某些情况下可能值得怀疑。我们提出了一种非参数方法,不要求任意离散,但涉及对仪器的连续分解进行扫描;将扫描统计数据结合起来,通过加权集成来估计未知参数。我们确定了拟议的综合估计器和整个仪器样本空间基本扫描过程的无症状常态性。模拟研究和对真实数据集的分析表明该方法对依赖任意离散或仪器时刻的程序的收益。