A Functional Varying-Coefficient Single-Index Model for Functional Response Data

References

• Basser, P. J., Mattiello, J., and LeBihan, D. (1994), “Estimation of the Effective Self-Diffusion Tensor From the NMR Spin Echo,” Journal of Magnetic Resonance, Series B, 103, 247–254.
   Web of Science ®Google Scholar
• Buzsaki, G. (2011). Rhythms of The Brain, Oxford, UK: Oxford University Press.
   Google Scholar
• Carroll, R. J., Fan, J., Gijbels, I., and Wand, M. P. (1997), “Generalized Partially Linear Single-Index Models,” Journal of the American Statistical Association, 92, 477–489.
   Web of Science ®Google Scholar
• Cheng, M. Y., Toshio, H., Li, J. and Peng, H. (2014), “Nonparametric Independence Screening and Structural Identification for Ultra-High Dimensional Longitudinal Data,” Annals of Statistics, 42, 1819–1849.
   Web of Science ®Google Scholar
• Cheng, M. Y., Zhang, W., and Chen, L. (2009), “Statistical Estimation in Generalized Multiparameter Likelihood Models,” Journal of the American Statistical Association, 104, 1179–1191.
   Web of Science ®Google Scholar
• Cui, X., Härdle, W. K., and Zhu, L. X. (2011), “The EFM Approach for Single-Index Models,” Annals of Statistics, 39, 1658–1688.
   Web of Science ®Google Scholar
• Fan, J. and Huang, T. (2005), “Profile Likelihood Inferences on Semiparametric Varying-Coefficient Partially Linear Models,” Bernoulli, 11, 1031–1057.
   Web of Science ®Google Scholar
• Fan, J., and Yao, Q. (1998), “Efficient Estimation of Conditional Variance Functions in Stochastic Regression,” Biometrika, 85, 645–660.
   Web of Science ®Google Scholar
• Fan, J., Yao, Q., and Cai, Z. (2003), “Adaptive Varying-Coefficient Linear Models,” Journal of the Royal Statistical Society, Series B, 65, 57–80.
   Google Scholar
• Fan, J., and Zhang, W. (1999), “Statistical Estimation in Varying Coefficient Models,” The Annals of Statistics, 27, 1491–1518.
   Web of Science ®Google Scholar
• ——— (2008), “Statistical Methods With Varying Coefficient Models,” Statistics and its Interface, 1, 179–195.
   PubMed Web of Science ®Google Scholar
• Friston, K. J. (2009), “Modalities, Modes, and Models in Functional Neuroimaging,” Science, 326, 399–403.
   PubMed Web of Science ®Google Scholar
• Hall, P., and Marron, J. S. (1990), “On Variance Estimation in Nonparametric Regression,” Biometrika, 77, 415–419.
   Web of Science ®Google Scholar
• Härdle, W., Hall, P., and Ichimura, H. (1993), “Optimal Smoothing in Single-Index Models,” Annals of Statistics, 21, 157–178.
   Web of Science ®Google Scholar
• Heywood, I., Cornelius, S., and Carver, S. (2006), An Introduction to Geographical Information Systems, Englewood Cliffs, NJ: Pearson Prentice Hall.
   Google Scholar
• Hoover, D. R., Rice, J. A., Wu, C. O., and Yang, L. P. (1998), “Nonparametric Smoothing Estimates of Time-Varying Coefficient Models With Longitudinal Data,” Biometrika, 85, 809–822.
   Web of Science ®Google Scholar
• Horowitz, J. L. (2009), Semiparametric and Nonparametric Methods in Econometrics, New York: Springer.
   Google Scholar
• Jiang, C. R., and Wang, J. L. (2010). “Covariate-Adjusted Functional Principal Components Analysis for Longitudinal Data,” The Annals of Statistics, 38, 1194–1226.
   Web of Science ®Google Scholar
• Ma, Y., and Zhu, L. (2013), “A Review on Dimension Reduction,” International Statistics Review, 81, 134–150.
   PubMed Web of Science ®Google Scholar
• Morris, J. S., and Carroll, R. J. (2006), “Wavelet-Based Functional Mixed Models,” Journal of the Royal Statistical Society, Series B, 68, 179–199.
   Google Scholar
• Niedermeyer, E., and da Silva, F. L. (2005), Electroencephalography: Basic Principles, Clinical Applications, and Related Fields, Baltimore, MD: Lippincot Williams & Wilkins.
   Google Scholar
• Ramsay, J. O., and Silverman, B. W. (2005), Functional Data Analysis, New York: Springer-Verlag.
   Google Scholar
• Smith, S. M., Jenkinson, M., Johansen-Berg, H., Rueckert, D., Nichols, T. E., Mackay, C. E., Watkins, K. E., Ciccarelli, O., Cader, M. Z., Matthews, P. M., and Behrens, T. E. J. (2006), “Tract-Based Spatial Statistics: Voxelwise Analysis of Multi-Subject Diffusion Data,” NeuroImage, 31, 1487–1505.
   PubMed Web of Science ®Google Scholar
• Towle, V. L., Bola nos, J., Suarez, D., Tan, K., Grzeszczuk, R., Levin, D. N., Cakmur, R., Frank, S. A., and Spire, J. P., (1993), “The Spatial Location of EEG Electrodes: Locating the Best-Fitting Sphere Relative to Cortical Anatomy,” Electroencephalogr Clin Neurophysiol, 86, 1–6.
   PubMedGoogle Scholar
• Wang, J. L., Xue, L., Zhu, L. and Chong, Y. S. (2010), “Estimation for a Partial-Linear Single-Index Model,” The Annals of Statistics, 1, 246–274.
   Web of Science ®Google Scholar
• Wang, L., Li, H., and Huang, J. Z. (2008), “Variable Selection in Nonparametric Varying-Coefficient Models for Analysis of Repeated Measurements,” Journal of the American Statistical Association, 103, 1556–1569.
   PubMed Web of Science ®Google Scholar
• Wang, Q., and Xue, L. (2011), “Statistical Inference in Partially-Varying-Coefficient Single-Index Model,” Journal of Multivariate Analysis, 102, 1–19.
   Web of Science ®Google Scholar
• Wong, H., Ip, W., and Zhang, R. (2008), “Varying-Coefficient Single-Index Model,” Computational Statistics and Data Analysis, 52, 1458–1476.
   Web of Science ®Google Scholar
• Wu, C. O., and Chiang, C. T. (2000), “Kernel Smoothing on Varying Coefficient Models With Longitudinal Dependent Variable,” Statistica Sinica, 10, 433–456.
   Web of Science ®Google Scholar
• Xia, Y. (2006), “Asymptotic Distributions for Two Estimators of the Single-Index Model,” Econometric Theory, 22, 1112–1137.
   Web of Science ®Google Scholar
• Xia, Y., Tong, H., Li, W., and Zhu, L. X. (2002), “An Adaptive Estimation of Dimension Reduction Space,” Journal of the Royal Statistical Society, Series B, 64, 363–410.
   Google Scholar
• Zhang, W. (2011), “Identification of the Constant Components in Generalised Semivarying Coefficient Models by Cross–Validation,” Statistica Sinica, 21, 1913–1929.
   Web of Science ®Google Scholar
• Zhu, H., Li, R., and Kong, L. (2012), “Multivariate Varying Coefficient Model for Functional Responses,” The Annals of Statistics, 40, 2634–2666.
   PubMed Web of Science ®Google Scholar
• Zhu, H., Zhang, H., Ibrahim, J. G., and Peterson, B. G. (2007), “Statistical Analysis of Diffusion Tensors in Diffusion-Weighted Magnetic Resonance Image Data” ( with discussion), Journal of the American Statistical Association, 102, 1085–1102.
   Web of Science ®Google Scholar