References
- Benatia, D., Carrasco, M., and Florens, J.-P. (2017), “Functional Linear Regression with Functional Response,” Journal of Econometrics, 201, 269–291. DOI: 10.1016/j.jeconom.2017.08.008.
- Bhattacharya, P. K., and Zhao, P.-L. (1997), “Semiparametric Inference in a Partial Linear Model,” The Annals of Statistics, 25, 244–262. DOI: 10.1214/aos/1034276628.
- Bissantz, N., Dette, H., Hildebrandt, T., and Bissantz, K. (2016), “Smooth Backfitting in Additive Inverse Regression,” Annals of the Institute of Statistical Mathematics, 68, 827–853. DOI: 10.1007/s10463-015-0517-x.
- Bosq, D. (2000), Linear Processes in Function Spaces, New York: Springer.
- Buja, A., Hastie, T., and Tibshirani, R. (1989), “Linear Smoothers and Additive Models,” (with discussion), The Annals of Statistics, 17, 453–555. DOI: 10.1214/aos/1176347115.
- Hall, P., and Horowitz, J. L. (2007), “Methodology and Convergence Rates for Functional Linear Regression,” The Annals of Statistics, 35, 70–91. DOI: 10.1214/009053606000000957.
- Han, K., and Park, B. U. (2018), “Smooth Backfitting for Errors-in-Variables Additive Models,” The Annals of Statistics, 46, 2216–2250. DOI: 10.1214/17-AOS1617.
- Han, K., Müller, H.-G., and Park, B. U. (2020), “Additive Functional Regression for Densities as Responses,” Journal of the American Statistical Association, 115, 997–1010. DOI: 10.1080/01621459.2019.1604365.
- Horváth, L., and Kokoszka, P. (2012), Inference for Functional Data with Applications, New York: Springer.
- Jeon, J. M., and Park, B. U. (2020), “Additive Regression with Hilbertian Responses,” The Annals of Statistics, 48, 2671–2697. DOI: 10.1214/19-AOS1902.
- Jeon, J. M., Park, B. U., and Van Keilegom, I. (2021), “Additive Regression with Non-Euclidean Responses and Predictors,” The Annals of Statistics, 49, 2611–2641. DOI: 10.1214/21-AOS2048.
- Jeon, J. M., and Van Bever, G. (2022), “Additive Regression with General Imperfect Variables,” arXiv:2212.05745.
- Lee, E. R., Han, K., and Park, B. U. (2018), “Estimation of Errors-in-Variables Partially Linear Additive Models,” Statistica Sinica, 28, 2353–2373.
- Lee, Y. K., Mammen, E., and Park, B. U. (2010), “Backfitting and Smooth Backfitting for Additive Quantile Models,” The Annals of Statistics, 38, 2857–2883. DOI: 10.1214/10-AOS808.
- Lee, Y. K., Mammen, E., and Park, B. U. (2012), “Flexible Generalized Varying Coefficient Regression Models,” The Annals of Statistics, 40, 1906–1933.
- Liang, H. (2006), “Estimation in Partially Linear Models and Numerical Comparisons,” Computational Statistics & Data Analysis, 50, 675–687. DOI: 10.1016/j.csda.2004.10.007.
- Liang, H., Thurston, S. W., Ruppert, D., Apanasovich, T., and Hauser, R. (2008), “Additive Partially Linear Models with Measurement Errors,” Biometrika, 95, 667–678. DOI: 10.1093/biomet/asn024.
- Lin, Z., Müller, H.-G., and Park, B. U. (2022), “Additive Models for Symmetric Positive-Definite Matrices and Lie Groups,” Biometrika (to appear). DOI: 10.1093/biomet/asac055.
- Linton, O., Sperlich, S., and van Keilegom, I. (2008), “Estimation of a Semiparametric Transformation Model,” The Annals of Statistics, 36, 686–718. DOI: 10.1214/009053607000000848.
- Mammen, E., Linton, O., and Nielsen, J. P. (1999), “The Existence and Asymptotic Properties of a Backfitting Projection Algorithm under Weak Conditions,” The Annals of Statistics, 27, 1443–1490. DOI: 10.1214/aos/1017939138.
- Opsomer, J. D., and Ruppert, D. (1997), “Fitting a Bivariate Additive Model by Local Polynomial Regression,” The Annals of Statistics, 25, 186–211. DOI: 10.1214/aos/1034276626.
- Opsomer, J. D., and Ruppert, D. (1999), “A Root-n Consistent Backfitting Estimator for Semiparametric Additive Modeling,” Journal of Computational and Graphical Statistics, 8, 715–732.
- Ramsay, J. O., and Silverman, B. W. (2005), Functional Data Analysis, New York: Springer.
- Severini, T., and Wong, W. (1992), “Profile Likelihood and Conditionally Parametric Models,” The Annals of Statistics, 20, 1768–1802. DOI: 10.1214/aos/1176348889.
- van de Geer, S. (2000), Empirical Processes in M-Estimation, Cambridge: Cambridge University Press.
- Yao, F., Müller, H.-G., and Wang, J.-L. (2005), “Functional Linear Regression Analysis for Longitudinal Data,” The Annals of Statistics, 33, 2873–2903. DOI: 10.1214/009053605000000660.
- Yu, K., Mammen, E., and Park, B. U. (2011), “Semi-Parametric Regression: Efficiency Gains from Modeling the Nonparametric Part,” Bernoulli, 17, 736–748. DOI: 10.3150/10-BEJ296.
- Yu, K., Park, B. U., and Mammen, E. (2008), “Smooth Backfitting in Generalized Additive Models,” The Annals of Statistics, 36, 228–260. DOI: 10.1214/009053607000000596.
- Zhang, X., Park, B. U., and Wang, J.-L. (2013), “Time-Varying Additive Models for Longitudinal Data,” Journal of the American Statistical Association, 108, 983–998. DOI: 10.1080/01621459.2013.778776.