Matrix completion under complex survey sampling

Xiaojun Mao (), Zhonglei Wang () and Shu Yang ()
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Xiaojun Mao: Shanghai Jiao Tong University
Zhonglei Wang: Xiamen University
Shu Yang: North Carolina State University

Annals of the Institute of Statistical Mathematics, 2023, vol. 75, issue 3, No 3, 463-492

Abstract: Abstract Multivariate nonresponse is often encountered in complex survey sampling, and simply ignoring it leads to erroneous inference. In this paper, we propose a new matrix completion method for complex survey sampling. Different from existing works either conducting row-wise or column-wise imputation, the data matrix is treated as a whole which allows for exploiting both row and column patterns simultaneously. A column-space-decomposition model is adopted incorporating a low-rank structured matrix for the finite population with easy-to-obtain demographic information as covariates. Besides, we propose a computationally efficient projection strategy to identify the model parameters under complex survey sampling. Then, an augmented inverse probability weighting estimator is used to estimate the parameter of interest, and the corresponding asymptotic upper bound of the estimation error is derived. Simulation studies show that the proposed estimator has a smaller mean squared error than other competitors, and the corresponding variance estimator performs well. The proposed method is applied to assess the health status of the U.S. population.

Keywords: Asymptotic upper bound; Augmented inverse probability weighting estimator; Low-rank structure; Missingness at random (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10463-022-00851-5

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