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Generalized regression estimators with concave penalties and a comparison to lasso type estimators

Author

Listed:
  • Elena McDonald

    (Archer Daniels Midland)

  • Xin Wang

    (San Diego State University)

Abstract

The generalized regression (GREG) estimator is usually used in survey sampling when incorporating auxiliary information. Generally, not all available covariates significantly contribute to the estimation process when there are multiple covariates. We propose two new GREG estimators based on concave penalties: one built from the smoothly clipped absolute deviation (SCAD) penalty and the other built from the minimax concave penalty (MCP). The performances of these estimators are compared to lasso-type estimators through a simulation study in a simple random sample (SRS) setting and a probability proportional to size (PPS) sample setting. It is shown that the proposed estimators produce improved estimates of the population total compared to that of the traditional GREG estimator and the estimators built from LASSO. Asymptotic properties are also derived for the proposed estimators. Bootstrap methods are also explored to improve coverage probability when the sample size is small.

Suggested Citation

  • Elena McDonald & Xin Wang, 2024. "Generalized regression estimators with concave penalties and a comparison to lasso type estimators," METRON, Springer;Sapienza Università di Roma, vol. 82(2), pages 213-239, August.
    • Handle: RePEc:spr:metron:v:82:y:2024:i:2:d:10.1007_s40300-023-00253-4
    DOI: 10.1007/s40300-023-00253-4
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    References listed on IDEAS

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