References
- Ait-Saïdi, A., F. Ferraty, R. Kassa, and P. Vieu. 2008. Cross-validated estimations in the single-functional index model. Statistics 42 (6):475–94. doi:https://doi.org/10.1080/02331880801980377.
- Aneiros, G., and A. Quintela. 2001. Asymptotic properties in partial linear models under dependence. Test 10 (2):333–55. doi:https://doi.org/10.1007/BF02595701.
- Bongiorno, E. G., E. Salinelli, A. Goia, and P. Vieu, eds. 2014. Contributions in infinite-dimensional statistics and related topics. Bologna: Societ editrice Esculapio. doi:https://doi.org/10.15651/9788874887637.
- Cai, T., and P. Hall. 2006. Prediction in functional linear regression. The Annals of Statistics 34 (5):2159–79. doi:https://doi.org/10.1214/009053606000000830.
- Cardot, H., F. Ferraty, and P. Sarda. 2003. Spline estimators for the functional linear model. Statistica Sinica 13:571–91.
- Chen, D., P. Hall, and H. G. Müller. 2011. Single and multiple index functional regression models with nonparametric link. The Annals of Statistics 39 (3):1720–47. doi:https://doi.org/10.1214/11-AOS882.
- Chen, K. H., and J. Lei. 2015. Localized functional principal component analysis. Journal of the American Statistical Association 110 (511):1266–75. doi:https://doi.org/10.1080/01621459.2015.1016225.
- Cui, X., H. Lin, and H. Lian. 2020. Partially functional linear regression in reproducing kernel Hilbert spaces. Computational Statistics & Data Analysis 150:106978. doi:https://doi.org/10.1016/j.csda.2020.106978.
- Dabo-Niang, S., and S. Guillas. 2010. Functional semiparametric partially linear model with autoregressive errors. Journal of Multivariate Analysis 101 (2):307–15. doi:https://doi.org/10.1016/j.jmva.2008.06.008.
- Davydov, N. 1968. Convergence of distributions generated by stationary stochastic processes. Theory of Probability & Its Applications 13 (4):691–96. doi:https://doi.org/10.1137/1113086.
- Du, J., X. Sun, R. Cao, and Z. Zhang. 2018. Statistical inference for partially linear additive spatial autoregressive models. Spatial Statistics 25:52–67. doi:https://doi.org/10.1016/j.spasta.2018.04.008.
- Du, J., Z. Zhang, and D. Xu. 2018. Estimation for the censored partially linear quantile regression models. Communications in Statistics - Simulation and Computation 47 (8):2393–408. doi:https://doi.org/10.1080/03610918.2017.1343842.
- Ferraty, F., A. Mas, and P. Vieu. 2007. Nonparametric regression on functional data: Inference and practical aspects. Australian & New Zealand Journal of Statistics 49 (3):267–86. doi:https://doi.org/10.1111/j.1467-842X.2007.00480.x.
- Ferraty, F., and P. Vieu. 2006. Nonparametric functional data analysis: Theory and practice. New York: Springer.
- Ferraty, F., W. G. Manteiga, A. M. Calvo, and P. Vieu. 2012. Presmoothing in functional linear regression. Statistica Sinica 22 (1):69–94. doi:https://doi.org/10.5705/ss.2010.085.
- He, G., H. G. Müller, and J. L. Wang. 2003. Functional canonical analysis for square integrable stochastic processes. Journal of Multivariate Analysis 85 (1):54–77. doi:https://doi.org/10.1016/S0047-259X(02)00056-8.
- HorváthL, L., and P. Kokoszka. 2012. Inference for functional data with applications. New York: Springer.
- Judge, G. G., W. E. Griffiths, R. C. Hill, H. Lütkepohl, and T. C. Lee. 1985. The theory and practice of econometrics. 2nd ed. Hoboken, NJ: Wiley.
- Kong, D., K. Xue, F. Yao, and H. Zhang. 2016. Partial functional linear regression in high dimension. Biometrika 103 (1):147–59. doi:https://doi.org/10.1093/biomet/asv062.
- Li, Y., N. Wang, and R. J. Carroll. 2013. Selecting the number of principal components in functional data. Journal of the American Statistical Association 108 (504):1284–94. doi:https://doi.org/10.1080/01621459.2013.788980.
- Lian, H. 2011. Functional partial linear model. Journal of Nonparametric Statistics 23 (1):115–28. doi:https://doi.org/10.1080/10485252.2010.500385.
- Lian, H. 2013. Shrinkage estimation and selection for multiple functional regression. Statistics Sinica 23:51–74.
- Mokkadem, A. 1988. Mixing properties of ARMA processes. Stochastic Processes and Their Applications 29 (2):309–15. doi:https://doi.org/10.1016/0304-4149(88)90045-2.
- Müller, H. G., and F. Yao. 2008. Functional additive models. Journal of the American Statistical Association 103 (484):1534–44. doi:https://doi.org/10.1198/016214508000000751.
- Müller, H. G., and F. Yao. 2010. Additive modeling of functional gradients. Biometrika 97 (4):791–806. doi:https://doi.org/10.1093/biomet/asq056.
- Ramsay, J. O., and B. W. Silverman. 2005. Functional data analysis. 2nd ed. New York: Springer.
- Riesz, F., and B. Sz-Nagy. 1955. Functional analysis. New York: Dover Publications.
- Roussas, G. G., L. T. Tran, and D. A. Ioannides. 1992. Fixed design regression for time series: Asymptotic normality. Journal of Multivariate Analysis 40 (2):262–91. doi:https://doi.org/10.1016/0047-259X(92)90026-C.
- Şentürk, D., and H.-G. Müller. 2010. Functional varying coefficient models for longitudinal data. Journal of the American Statistical Association 105 (491):1256–64. doi:https://doi.org/10.1198/jasa.2010.tm09228.
- Shin, H. 2009. Partial functional linear regression. Journal of Statistical Planning and Inference 139 (10):3405–18. doi:https://doi.org/10.1016/j.jspi.2009.03.001.
- Silverman, B. W. 1996. Smoothed functional principal components analysis by choice of norm. The Annals of Statistics 24 (1):1–24. doi:https://doi.org/10.1214/aos/1033066196.
- Wang, G. C., X. N. Feng, and M. Chen. 2016. Functional partial linear single-index model. Scandinavian Journal of Statistics 43 (1):261–74. doi:https://doi.org/10.1111/sjos.12178.
- Wang, G. C., Y. Su, and L. J. Shu. 2016. One-day-ahead daily power forecasting of photovoltaic systems based on partial functional linear regression models. Renewable Energy 96:469–78. doi:https://doi.org/10.1016/j.renene.2016.04.089.
- Wang, G., N. Lin, and B. Zhang. 2013. Dimension reduction in functional regression using mixed data canonical correlation analysis. Statistics and Its Interface 6 (2):187–96. doi:https://doi.org/10.4310/SII.2013.v6.n2.a3.
- Wang, M., M. L. Shu, J. J. Zhou, and S. X. Wu. 2020. Least square estimation for multiple functional linear model with autoregressive errors. Acta Mathematica Application Sinica (Enlish Series). Manuscript Accepted.
- Wise, J. 1955. The autocorrelation function and the spectral density function. Biometrika 42 (1–2):151–9. doi:https://doi.org/10.2307/2333432.
- Wu, Y., J. Fan, and H. G. Müller. 2010. Varying-coefficient functional linear regression. Bernoulli 16 (3):730–58. doi:https://doi.org/10.3150/09-BEJ231.
- Yao, F., and H. G. Müller. 2010. Functional quadratic regression. Biometrika 97 (1):49–64. doi:https://doi.org/10.1093/biomet/asp069.
- Yao, F., H. G. Müller, and J. L. Wang. 2005. Functional data analysis for sparse longitudinal data. Journal of the American Statistical Association 100 (470):577–90. doi:https://doi.org/10.1198/016214504000001745.
- Yu, P., J. Du, and Z. Zhang. 2017. Varying-coefficient partially functional linear quantile regression models. Journal of the Korean Statistical Society 46 (3):462–75. doi:https://doi.org/10.1016/j.jkss.2017.02.001.
- Zhou, J., Z. Chen, and Q. Peng. 2016. Polynomial spline estimation for partial functional linear regression models. Computational Statistics 31 (3):1107–29. doi:https://doi.org/10.1007/s00180-015-0636-0.
- Zhu, H. R., Zhang, Z. Yu, H. Lian, and Y. Liu. 2019. Estimation and testing for partial functional linear errors-in-variables models. Journal of Multivariate Analysis 170:296–314. doi:https://doi.org/10.1016/j.jmva.2018.11.005.
- Zipunnikov, V., B. Caffo, D. M. Yousem, C. Davatzikos, B. S. Schwartz, and C. Crainiceanu. 2011. Multilevel functional principal component analysis for high-dimensional data. Journal of Computational and Graphical Statistics : A Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America 20 (4):852–73. doi:https://doi.org/10.1198/jcgs.2011.10122.