Causal Inference with Corrupted Data: Measurement Error, Missing Values, Discretization, and Differential Privacy
This work addresses the trade-off between data privacy and analysis precision, particularly for Census data, but is incremental as it builds on existing methods in matrix completion and semiparametric statistics.
The authors tackled the problem of causal inference with corrupted data, such as measurement error and missing values, by proposing a semiparametric model and a data cleaning procedure with adjusted confidence intervals, achieving a rate of n^{1/2} for semiparametric estimands and validating results through simulations.
The US Census Bureau will deliberately corrupt data sets derived from the 2020 US Census, enhancing the privacy of respondents while potentially reducing the precision of economic analysis. To investigate whether this trade-off is inevitable, we formulate a semiparametric model of causal inference with high dimensional corrupted data. We propose a procedure for data cleaning, estimation, and inference with data cleaning-adjusted confidence intervals. We prove consistency and Gaussian approximation by finite sample arguments, with a rate of $n^{ 1/2}$ for semiparametric estimands that degrades gracefully for nonparametric estimands. Our key assumption is that the true covariates are approximately low rank, which we interpret as approximate repeated measurements and empirically validate. Our analysis provides nonasymptotic theoretical contributions to matrix completion, statistical learning, and semiparametric statistics. Calibrated simulations verify the coverage of our data cleaning adjusted confidence intervals and demonstrate the relevance of our results for Census-derived data.