Estimation of a functional single index model with dependent errors and unknown error density

References

• Ait-Saïdi, A., F. Ferraty, R. Kassa, and P. Vieu. 2008. Cross-validated estimations in the single-functional index model. Statistics: A Journal of Theoretical and Applied Statistics 42 (6):475–94.
   Google Scholar
• Akritas, M. G., and I. Van Keilegom. 2001. Non-parametric estimation of the residual distribution. Scandinavian Journal of Statistics 28 (3):549–67.
   Web of Science ®Google Scholar
• Benhenni, K., F. Ferraty, M. Rachdi, and P. Vieu. 2007. Local smoothing regression with functional data. Computational Statistics 22 (3):353–69.
   Web of Science ®Google Scholar
• Besse, P. C., H. Cardot, and D. B. Stephenson. 2000. Autoregressive forecasting of some functional climatic variations. Scandinavian Journal of Statistics 27 (4):673–87.
   Web of Science ®Google Scholar
• Burba, F., F. Ferraty, and P. Vieu. 2009. k-nearest neighbour method in functional nonparametric regression. Journal of Nonparametric Statistics 21 (4):453–69.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• Davis, R. A., P. Zang, and T. Zheng. 2016. Sparse vector autoregressive modeling. Journal of Computational and Graphical Statistics 25 (4):1077–96.
   Web of Science ®Google Scholar
• Efromovich, S. 2005. Estimation of the density of regression errors. The Annals of Statistics 33 (5):2194–227.
   Web of Science ®Google Scholar
• Escanciano, J. C., and D. T. Jacho-Chávez. 2012. n Uniformly consistent density estimation in nonparametric regression models. Journal of Econometrics 167 (2):305–16.
   Web of Science ®Google Scholar
• Fan, J., and I. Gijbels. 1996. Local polynomial modelling and its applications. London: Chapman & Hall/CRC.
   Google Scholar
• Fan, Y., G. M. James, and P. Radchenko. 2015. Functional additive regression. The Annals of Statistics 43 (5):2296–325.
   Web of Science ®Google Scholar
• Febrero-Bande, M., P. Galeano, and W. González-Manteiga. 2017. Functional principal component regression and functional partial least-squares regression: An overview and a comparative study. International Statistical Review 85 (1):61–83.
   Web of Science ®Google Scholar
• Ferraty, F., A. Laksaci, and P. Vieu. 2005. Functional time series prediction via conditional mode estimation. Comptes Rendus Mathematique 340 (5):389–92.
   Web of Science ®Google Scholar
• Ferraty, F., J. Park, and P. Vieu. 2011. Estimation of a functional single index model. In F. Ferraty (Ed.), Recent advances in functional data analysis and related topics. Contributions to Statistics, pp. 111–116. Berlin, New York: Springer.
   Google Scholar
• Ferraty, F., A. Peuch, and P. Vieu. 2003. Single functional index model. Comptes Rendus Mathematique 336 (12):1025–8.
   Web of Science ®Google Scholar
• Ferraty, F., A. Rabhi, and P. Vieu. 2005. Conditional quantiles for dependent functional data with application to the climatic El niño phenomenon. Sankhya: The Indian Journal of Statistics 67 (2):378–98.
   Google Scholar
• Ferraty, F., and P. Vieu. 2006. Nonparametric functional data analysis: Theory and practice. New York: Springer.
   Google Scholar
• Garthwaite, P. H., Y. Fan, and S. A. Sisson. 2016. Adaptive optimal scaling of Metropolis-Hastings algorithms using the Robbins-Monro process. Communications in Statistics-Theory and Methods 45 (17):5098–111.
   Web of Science ®Google Scholar
• Geweke, J. 1992. Evaluating the accuracy of sampling-based apapproach to calculating posterior moments. In J. M. Bernardo, J. Berger, A. P. Dawid, and J. F. M. Smith (Eds.), Bayesian statistics. pp. 169–193. Oxford: Clarendon Press.
   Google Scholar
• Geweke, J. 2010. Complete and incomplete econometric models. Princeton, NJ: Princeton University Press.
   Google Scholar
• Geweke, J. F. 1999. Using simulation methods for bayesian econometric models: Inference, development, and communication. Econometric Reviews 18 (1):1–73.
   Google Scholar
• Gilks, W. R., S. Richardson, and D. J. Spiegelhalter. 1996. Markov chain Monte Carlo in practice. London: Chapman & Hall.
   Google Scholar
• Goia, A., and P. Vieu. 2015. A partitioned single functional index model. Computational Statistics 30 (3):673–92.
   Web of Science ®Google Scholar
• Heidelberger, P., and P. D. Welch. 1983. Simulation run length control in the presence of an initial transient. Operations Research 31 (6):1109–44.
   Web of Science ®Google Scholar
• Hurvich, C. M., and C.-L. Tsai. 1989. Regression and time series model selection in small samples. Biometrika 76 (2):297–307.
   Web of Science ®Google Scholar
• Hyndman, R. J., and H. L. Shang. 2010. Rainbow plots, bagplots, and boxplots for functional data. Journal of Computational and Graphical Statistics 19 (1):29–45.
   Web of Science ®Google Scholar
• James, G. M., and B. W. Silverman. 2005. Functional adaptive model estimation. Journal of the American Statistical Association 100 (470):565–76.
   Web of Science ®Google Scholar
• Jiang, C.-R., and J.-L. Wang. 2011. Functional single index models for longitudinal data. The Annals of Statistics 39 (1):362–88.
   Web of Science ®Google Scholar
• Jones, M. C., J. S. Marron, and B. U. Park. 1991. A simple root-n bandwidth selector. The Annals of Statistics 19(4):1919–32.
   Web of Science ®Google Scholar
• Kalivas, J. H. 1997. Two data sets of near infrared spectra. Chemometrics and Intelligent Laborary Systems 37 (2):255–9.
   Web of Science ®Google Scholar
• Kim, S., N. Shepherd, and S. Chib. 1998. Stochastic volatility: Likelihood inference and comparison with ARCH models. Review of Economic Studies 65 (3):361–93.
   Web of Science ®Google Scholar
• Marron, J. S., and M. P. Wand. 1992. Exact mean integrated squared error. The Annals of Statistics 20 (2):712–36.
   Web of Science ®Google Scholar
• Meyer, R., and J. Yu. 2000. BUGS for a Bayesian analysis of stochastic volatility models. The Econometrics Journal 3 (2):198–215.
   Google Scholar
• Morris, J. S. 2015. Functional regression. Annual Review of Statistics and Its Application 2 (1):321–59.
   Web of Science ®Google Scholar
• MüLler, H.-G., and J.-L. Wang. 1990. Locally adaptive hazard smoothing. Probability Theory and Related Fields 85 (4):523–38.
   Web of Science ®Google Scholar
• Neumeyer, N., and H. Dette. 2007. Testing for symmetric error distribution in nonparametric regression models. Statistica Sinica 17 (2):775–95.
   Web of Science ®Google Scholar
• Plummer, M., N. Best, K. Cowles, and K. Vines. 2006. CODA: Convergence diagnosis and output analysis for MCMC. R News 6 (1):7–11.
   Google Scholar
• Quintela-del-Río, A., and M. Francisco-Fernández. 2011. Nonparametric functional data estimation applied to ozone data: Prediction and extreme value analysis. Chemosphere 82 (6):800–8.
   PubMed Web of Science ®Google Scholar
• R Core Team 2018. R: a language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. https://www.R-project.org/.
   Google Scholar
• Rachdi, M., and P. Vieu. 2007. Nonparametric regression for functional data: Automatic smoothing parameter selection. Journal of Statistical Planning and Inference 137 (9):2784–801.
   Web of Science ®Google Scholar
• Reiss, P., and R. T. Ogden. 2009. Smoothing parameter selection for a class of semiparametric linear models. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 71 (2):505–23.
   Web of Science ®Google Scholar
• Reiss, P. T., J. Goldsmith, H. L. Shang, and R. T. Ogden. 2017. Methods for scalar-on-function regression. International Statistical Review 85 (2):228–49.
   PubMed Web of Science ®Google Scholar
• Reiss, P. T., and R. T. Ogden. 2007. Functional principal component regression and functional partial least squares. Journal of the American Statistical Association 102 (479):984–96.
   Web of Science ®Google Scholar
• Robbins, H., and S. Monro. 1951. A stochastic approximation method. The Annals of Mathematical Statistics 22 (3):400–7.
   Google Scholar
• Robert, C. P., and G. Casella. 2010. Introducing Monte Carlo methods with R. New York: Springer.
   Google Scholar
• Roberts, G. O., and J. S. Rosenthal. 2009. Examples of adaptive MCMC. Journal of Computational and Graphical Statistics 18 (2):349–67.
   Web of Science ®Google Scholar
• Shang, H. L. 2013. Bayesian bandwidth estimation for a nonparametric functional regression model with unknown error density. Computational Statistics and Data Analysis 67 :185–98.
   Web of Science ®Google Scholar
• Shang, H. L. 2014a. Bayesian bandwidth estimation for a functional nonparametric regression model with mixed types of regressors and unknown error density. Journal of Nonparametric Statistics 26 (3):599–615.
   Web of Science ®Google Scholar
• Shang, H. L. 2014b. Bayesian bandwidth estimation for a semi-functional partial linear regression model with unknown error density. Computational Statistics 29 (3–4):829–48.
   Web of Science ®Google Scholar
• Shang, H. L. 2016. A bayesian approach for determining the optimal semi-metric and bandwidth in scalar-on-funciton quantile regression with unknown error density and dependent functional data. Journal of Multivariate Analysis 146:95–104.
   Web of Science ®Google Scholar
• Shang, H. L., and R. J. Hyndman. 2013. Fds: Functional data sets. University of Southampton. R package version 1.7. URL: https://CRAN.R-project.org/package=fds.
   Google Scholar
• Zhang, X., R. D. Brooks, and M. L. King. 2009. A Bayesian approach to bandwidth selection for multivariate kernel regression with an application to state-price density estimation. Journal of Econometrics 153 (1):21–32.
   Web of Science ®Google Scholar
• Zhang, X., M. L. King, and H. L. Shang. 2014. A sampling algorithm for bandwidth estimation in an nonparametric regression model with a flexible error density. Computational Statistics and Data Analysis 78:218–34.
   Web of Science ®Google Scholar