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A Mallows-Type Model Averaging Estimator for the Varying-Coefficient Partially Linear Model

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  • Rong Zhu
  • Alan T. K. Wan
  • Xinyu Zhang
  • Guohua Zou

Abstract

In the last decade, significant theoretical advances have been made in the area of frequentist model averaging (FMA); however, the majority of this work has emphasized parametric model setups. This article considers FMA for the semiparametric varying-coefficient partially linear model (VCPLM), which has gained prominence to become an extensively used modeling tool in recent years. Within this context, we develop a Mallows-type criterion for assigning model weights and prove its asymptotic optimality. A simulation study and a real data analysis demonstrate that the FMA estimator that arises from this criterion is vastly preferred to information criterion score-based model selection and averaging estimators. Our analysis is complicated by the fact that the VCPLM is subject to uncertainty arising not only from the choice of covariates, but also whether the covariate should enter the parametric or nonparametric parts of the model. Supplementary materials for this article are available online.

Suggested Citation

  • Rong Zhu & Alan T. K. Wan & Xinyu Zhang & Guohua Zou, 2019. "A Mallows-Type Model Averaging Estimator for the Varying-Coefficient Partially Linear Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 882-892, April.
    • Handle: RePEc:taf:jnlasa:v:114:y:2019:i:526:p:882-892
    DOI: 10.1080/01621459.2018.1456936
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    Citations

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    Cited by:

    1. Giuseppe De Luca & Jan Magnus & Franco Peracchi, 2022. "Asymptotic properties of the weighted average least squares (WALS) estimator," Tinbergen Institute Discussion Papers 22-022/III, Tinbergen Institute.
    2. Guozhi Hu & Weihu Cheng & Jie Zeng, 2023. "Optimal Model Averaging for Semiparametric Partially Linear Models with Censored Data," Mathematics, MDPI, vol. 11(3), pages 1-21, February.
    3. Fang, Fang & Liu, Minhan, 2020. "Limit of the optimal weight in least squares model averaging with non-nested models," Economics Letters, Elsevier, vol. 196(C).
    4. Xiaochao Xia, 2021. "Model averaging prediction for nonparametric varying-coefficient models with B-spline smoothing," Statistical Papers, Springer, vol. 62(6), pages 2885-2905, December.
    5. Yuying Sun & Shaoxin Hong & Zongwu Cai, 2023. "Optimal Local Model Averaging for Divergent-Dimensional Functional-Coefficient Regressions," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202309, University of Kansas, Department of Economics, revised Sep 2023.
    6. Jingwen Tu & Hu Yang & Chaohui Guo & Jing Lv, 2021. "Model averaging marginal regression for high dimensional conditional quantile prediction," Statistical Papers, Springer, vol. 62(6), pages 2661-2689, December.
    7. Mark F. J. Steel, 2020. "Model Averaging and Its Use in Economics," Journal of Economic Literature, American Economic Association, vol. 58(3), pages 644-719, September.
    8. Miaomiao Wang & Xinyu Zhang & Alan T. K. Wan & Kang You & Guohua Zou, 2023. "Jackknife model averaging for high‐dimensional quantile regression," Biometrics, The International Biometric Society, vol. 79(1), pages 178-189, March.
    9. Yuting Wei & Qihua Wang & Wei Liu, 2021. "Model averaging for linear models with responses missing at random," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 535-553, June.
    10. Longbiao Liao & Jinghao Liu, 2024. "Model Averaging for Accelerated Failure Time Models with Missing Censoring Indicators," Mathematics, MDPI, vol. 12(5), pages 1-16, February.
    11. Fang, Fang & Yu, Zhou, 2020. "Model averaging assisted sufficient dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    12. Zishu Zhan & Yang Li & Yuhong Yang & Cunjie Lin, 2023. "Model averaging for semiparametric varying coefficient quantile regression models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(4), pages 649-681, August.
    13. Fang, Fang & Li, Jialiang & Xia, Xiaochao, 2022. "Semiparametric model averaging prediction for dichotomous response," Journal of Econometrics, Elsevier, vol. 229(2), pages 219-245.
    14. Denis Chetverikov, 2024. "Tuning parameter selection in econometrics," Papers 2405.03021, arXiv.org.
    15. Yuan, Chaoxia & Fang, Fang & Ni, Lyu, 2022. "Mallows model averaging with effective model size in fragmentary data prediction," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    16. Wei, Yuting & Wang, Qihua, 2021. "Cross-validation-based model averaging in linear models with response missing at random," Statistics & Probability Letters, Elsevier, vol. 171(C).
    17. Fang, Fang & Yang, Qiwei & Tian, Wenling, 2022. "Cross-validation for selecting the penalty factor in least squares model averaging," Economics Letters, Elsevier, vol. 217(C).
    18. Jie Zeng & Weihu Cheng & Guozhi Hu, 2023. "Optimal Model Averaging Estimation for the Varying-Coefficient Partially Linear Models with Missing Responses," Mathematics, MDPI, vol. 11(8), pages 1-21, April.

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