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Penalized multiply robust estimation in high-order autoregressive processes with missing explanatory variables

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  • Xiong, Wei
  • Wang, Dehui
  • Deng, Dianliang
  • Wang, Xinyang
  • Zhang, Wanying

Abstract

Multiply robust estimation with missing data is considered as an important field in statistics, which incorporates information by weighting multiply candidate models and loosens the requirement of the model specification. Nevertheless, in high-dimensional cases one more flexible hypothesis is the “true structure” beyond the correct model. In this paper, we study the parametric estimation for high-order autoregressive processes with a lagged-dependent binary explanatory variable that is missing at random (MAR). Based on the “true structure” specification, we propose a penalized multiply robust estimation equation in the presence of multiply candidate model sets. The selecting criterion for optimal tuning parameters is modified for the model identification with incomplete data. We validate that our tuning criterion can correctly distinguish the true autoregressive coefficients from zero asymptotically, the estimators of population parameters enjoy the oracle properties as well. Some simulations are carried out and we apply the method to fit the model for the U.S. Industrial Production Index data and produce out-of-sample forecasts to confirm the rationality of results.

Suggested Citation

  • Xiong, Wei & Wang, Dehui & Deng, Dianliang & Wang, Xinyang & Zhang, Wanying, 2022. "Penalized multiply robust estimation in high-order autoregressive processes with missing explanatory variables," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    • Handle: RePEc:eee:jmvana:v:187:y:2022:i:c:s0047259x21001457
    DOI: 10.1016/j.jmva.2021.104867
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    References listed on IDEAS

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    1. Peisong Han & Lu Wang, 2013. "Estimation with missing data: beyond double robustness," Biometrika, Biometrika Trust, vol. 100(2), pages 417-430.
    2. Wei Li & Yuwen Gu & Lan Liu, 0. "Demystifying a class of multiply robust estimators," Biometrika, Biometrika Trust, vol. 107(4), pages 919-933.
    3. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    4. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    5. Hansheng Wang & Guodong Li & Chih‐Ling Tsai, 2007. "Regression coefficient and autoregressive order shrinkage and selection via the lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(1), pages 63-78, February.
    6. Hansheng Wang & Runze Li & Chih-Ling Tsai, 2007. "Tuning parameter selectors for the smoothly clipped absolute deviation method," Biometrika, Biometrika Trust, vol. 94(3), pages 553-568.
    7. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    8. Peisong Han, 2014. "Multiply Robust Estimation in Regression Analysis With Missing Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1159-1173, September.
    9. Jianhua Z. Huang & Lijian Yang, 2004. "Identification of non‐linear additive autoregressive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(2), pages 463-477, May.
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