Matrix Completion, Counterfactuals, and Factor Analysis of Missing Data

This article proposes an imputation procedure that uses the factors estimated from a tall block along with the re-rotated loadings estimated from a wide block to impute missing values in a panel of data. Assuming that a strong factor structure holds for the full panel of data and its sub-blocks, it...

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Vydáno v:Journal of the American Statistical Association Ročník 116; číslo 536; s. 1746 - 1763
Hlavní autoři: Bai, Jushan, Ng, Serena
Médium: Journal Article
Jazyk:angličtina
Vydáno: Alexandria Taylor & Francis 02.10.2021
Taylor & Francis Ltd
Témata:
Convergence
Counterfactual thinking
Counterfactuals
EM algorithm
Error analysis
Estimation
Factor analysis
Hypothesis testing
mathematical theory
Matrices
Missing data
Missing-at-random
Normal distribution
Nuclear-norm regularization
Regression analysis
Regularization
Statistical methods
Statistics
Synthetic controls
ISSN:0162-1459, 1537-274X, 1537-274X
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Shrnutí:This article proposes an imputation procedure that uses the factors estimated from a tall block along with the re-rotated loadings estimated from a wide block to impute missing values in a panel of data. Assuming that a strong factor structure holds for the full panel of data and its sub-blocks, it is shown that the common component can be consistently estimated at four different rates of convergence without requiring regularization or iteration. An asymptotic analysis of the estimation error is obtained. An application of our analysis is estimation of counterfactuals when potential outcomes have a factor structure. We study the estimation of average and individual treatment effects on the treated and establish a normal distribution theory that can be useful for hypothesis testing.
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ISSN:0162-1459
1537-274X
1537-274X
DOI:10.1080/01621459.2021.1967163