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Matrix completion under complex survey sampling.

Xiaojun Mao1, Zhonglei Wang2, Shu Yang3

  • 1School of Mathematical Sciences, Ministry of Education Key Laboratory of Scientific and Engineering Computing, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China.

Annals of the Institute of Statistical Mathematics
|August 30, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces a novel matrix completion method for complex survey sampling to address multivariate nonresponse. The new approach improves estimation accuracy, outperforming existing methods in simulations for health status assessment.

Keywords:
Asymptotic upper boundAugmented inverse probability weighting estimatorLow-rank structureMissingness at random

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Area of Science:

  • Statistics
  • Survey Methodology
  • Data Science

Background:

  • Multivariate nonresponse is a significant challenge in complex survey sampling, leading to biased inferences if ignored.
  • Existing imputation methods often focus on row-wise or column-wise approaches, failing to leverage the full data structure.

Purpose of the Study:

  • To propose a new matrix completion method for complex survey sampling that simultaneously exploits row and column patterns.
  • To develop a computationally efficient method for parameter identification and estimation under complex survey designs.
  • To provide a robust estimator for parameters of interest with a derived error bound.

Main Methods:

  • A column-space-decomposition model is employed, treating the data matrix as a whole to capture simultaneous row and column patterns.
  • A low-rank structured matrix incorporating demographic covariates is used for the finite population.
  • An augmented inverse probability weighting estimator is utilized for parameter estimation.

Main Results:

  • The proposed matrix completion method demonstrated superior performance with a smaller mean squared error compared to existing competitors in simulation studies.
  • The derived variance estimator for the proposed method performed well, indicating reliability.
  • The method was successfully applied to assess the health status of the U.S. population.

Conclusions:

  • The novel matrix completion method effectively addresses multivariate nonresponse in complex surveys by utilizing the entire data matrix.
  • The proposed approach offers improved estimation accuracy and reliable variance estimation for survey data.
  • This method provides a valuable tool for analyzing complex survey data, as demonstrated by its application to U.S. health status assessment.