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Predictive functional linear models with diverging number of semiparametric single-index interactions

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  • Liu, Yanghui
  • Li, Yehua
  • Carroll, Raymond J.
  • Wang, Naisyin

Abstract

When predicting crop yield using both functional and multivariate predictors, the prediction performances benefit from the inclusion of the interactions between the two sets of predictors. We assume the interaction depends on a nonparametric, single-index structure of the multivariate predictor and reduce each functional predictor’s dimension using functional principal component analysis (FPCA). Allowing the number of FPCA scores to diverge to infinity, we consider a sequence of semiparametric working models with a diverging number of predictors, which are FPCA scores with estimation errors. We show that the parametric component of the model is root-n consistent and asymptotically normal, the overall prediction error is dominated by the estimation of the nonparametric interaction function, and justify a CV-based procedure to select the tuning parameters.

Suggested Citation

  • Liu, Yanghui & Li, Yehua & Carroll, Raymond J. & Wang, Naisyin, 2022. "Predictive functional linear models with diverging number of semiparametric single-index interactions," Journal of Econometrics, Elsevier, vol. 230(2), pages 221-239.
    • Handle: RePEc:eee:econom:v:230:y:2022:i:2:p:221-239
    DOI: 10.1016/j.jeconom.2021.03.010
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    1. Müller, Hans-Georg & Yao, Fang, 2008. "Functional Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1534-1544.
    2. Crainiceanu, Ciprian M. & Staicu, Ana-Maria & Di, Chong-Zhi, 2009. "Generalized Multilevel Functional Regression," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1550-1561.
    3. Li, Yehua & Wang, Naisyin & Carroll, Raymond J., 2010. "Generalized Functional Linear Models With Semiparametric Single-Index Interactions," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 621-633.
    4. Yu Y. & Ruppert D., 2002. "Penalized Spline Estimation for Partially Linear Single-Index Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1042-1054, December.
    5. Jianqing Fan & Qiwei Yao & Zongwu Cai, 2003. "Adaptive varying‐coefficient linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 57-80, February.
    6. Ping Yu & Zhongzhan Zhang & Jiang Du, 2016. "A test of linearity in partial functional linear regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(8), pages 953-969, November.
    7. Victor Chernozhukov & Juan Carlos Escanciano & Hidehiko Ichimura & Whitney K. Newey & James M. Robins, 2022. "Locally Robust Semiparametric Estimation," Econometrica, Econometric Society, vol. 90(4), pages 1501-1535, July.
    8. Zhou, Lan & Huang, Jianhua Z. & Martinez, Josue G. & Maity, Arnab & Baladandayuthapani, Veerabhadran & Carroll, Raymond J., 2010. "Reduced Rank Mixed Effects Models for Spatially Correlated Hierarchical Functional Data," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 390-400.
    9. Yuhang Xu & Yehua Li & Dan Nettleton, 2018. "Nested Hierarchical Functional Data Modeling and Inference for the Analysis of Functional Plant Phenotypes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 593-606, April.
    10. Cai, Zongwu & Juhl, Ted & Yang, Bingduo, 2015. "Functional index coefficient models with variable selection," Journal of Econometrics, Elsevier, vol. 189(2), pages 272-284.
    11. Yao, Fang & Muller, Hans-Georg & Wang, Jane-Ling, 2005. "Functional Data Analysis for Sparse Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 577-590, June.
    12. Hansen, James W., 2002. "Realizing the potential benefits of climate prediction to agriculture: issues, approaches, challenges," Agricultural Systems, Elsevier, vol. 74(3), pages 309-330, December.
    13. Xia, Yingcun, 2006. "Asymptotic Distributions For Two Estimators Of The Single-Index Model," Econometric Theory, Cambridge University Press, vol. 22(6), pages 1112-1137, December.
    14. Raymond K. W. Wong & Yehua Li & Zhengyuan Zhu, 2019. "Partially Linear Functional Additive Models for Multivariate Functional Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 406-418, January.
    15. Nicoleta Serban & Ana-Maria Staicu & Raymond J. Carroll, 2013. "Multilevel Cross-Dependent Binary Longitudinal Data," Biometrics, The International Biometric Society, vol. 69(4), pages 903-913, December.
    16. Gareth M. James, 2002. "Generalized linear models with functional predictors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 411-432, August.
    17. Hongxiao Zhu & Fang Yao & Hao Helen Zhang, 2014. "Structured functional additive regression in reproducing kernel Hilbert spaces," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(3), pages 581-603, June.
    18. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
    19. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76, Elsevier.
    20. Xia, Yingcun & Härdle, Wolfgang, 2006. "Semi-parametric estimation of partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1162-1184, May.
    21. Peter Hall & Mohammad Hosseini‐Nasab, 2006. "On properties of functional principal components analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 109-126, February.
    22. Dehan Kong & Kaijie Xue & Fang Yao & Hao H. Zhang, 2016. "Partially functional linear regression in high dimensions," Biometrika, Biometrika Trust, vol. 103(1), pages 147-159.
    23. Zhu, Hanbing & Zhang, Riquan & Yu, Zhou & Lian, Heng & Liu, Yanghui, 2019. "Estimation and testing for partially functional linear errors-in-variables models," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 296-314.
    24. Clara Happ & Sonja Greven, 2018. "Multivariate Functional Principal Component Analysis for Data Observed on Different (Dimensional) Domains," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 649-659, April.
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