Simultaneous inference for the mean function based on dense functional data

References

• Benko , M. , Härdle , W. and Kneip , A. 2009 . ‘Common Functional Principal Components’ . The Annals of Statistics , 37 : 1 – 34 .
   Web of Science ®Google Scholar
• Bunea , F. , Ivanescu , A. E. and Wegkamp , M. 2011 . ‘Adaptive Inference for the Mean of a Gaussian Process in Functional Data’ . Journal of the Royal Statistical Society. Series B , 73 : 531 – 558 .
   Google Scholar
• Cardot , H. 2000 . ‘Nonparametric Estimation of Smoothed Principal Components Analysis of Sampled Noisy Functions’ . Journal of Nonparametric Statistics , 12 : 503 – 538 .
   Web of Science ®Google Scholar
• Csőrgő , M. and Révész , P. 1981 . Strong Approximations in Probability and Statistics , New York : Academic Press .
   Google Scholar
• Cuevas , A. , Febrero , M. and Fraiman , R. 2006 . ‘On the Use of the Bootstrap for Estimating Functions with Functional Data’ . Computational Statistics and Data Analysis , 51 : 1063 – 1074 .
   Web of Science ®Google Scholar
• de Boor , C. 2001 . A Practical Guide to Splines , New York : Springer-Verlag .
   Google Scholar
• Degras , D. A. 2011 . ‘Simultaneous Confidence Bands for Nonparametric Regression with Functional Data’ . Statistica Sinica , 21 : 1735 – 1765 .
   Web of Science ®Google Scholar
• DeVore , R. and Lorentz , G. 1993 . Constructive Approximation: Polynomials and Splines Approximation , Berlin : Springer-Verlag .
   Google Scholar
• Fan , J. and Lin , S.-K. 1998 . ‘Tests of Significance When Data are Curves’ . Journal of the American Statistical Association , 93 : 1007 – 1021 .
   Web of Science ®Google Scholar
• Ferraty , F. and Vieu , P. 2006 . Nonparametric Functional Data Analysis: Theory and Practice , Berlin : Springer . Springer Series in Statistics
   Google Scholar
• Hall , P. , Müller , H. G. and Wang , J. L. 2006 . ‘Properties of Principal Component Methods for Functional and Longitudinal Data Analysis’ . The Annals of Statistics , 34 : 1493 – 1517 .
   Web of Science ®Google Scholar
• Huang , J. and Yang , L. 2004 . ‘Identification of Nonlinear Additive Autoregressive Models’ . Journal of the Royal Statistical Society. Series B , 66 : 463 – 477 .
   Google Scholar
• Li , Y. and Hsing , T. 2010a . ‘Uniform Convergence Rates for Nonparametric Regression and Principal Component Analysis in Functional/Longitudinal Data’ . The Annals of Statistics , 38 : 3321 – 3351 .
   Web of Science ®Google Scholar
• Li , Y. and Hsing , T. 2010b . ‘Deciding the Dimension of Effective Dimension Reduction Space for Functional and High-Dimensional Data’ . The Annals of Statistics , 38 : 3028 – 3062 .
   Web of Science ®Google Scholar
• Li , B. and Yu , Q. 2008 . ‘Classification of Functional Data: A Segmentation Approach’ . Computational Statistics and Data Analysis , 52 : 4790 – 4800 .
   Web of Science ®Google Scholar
• Liu , R. and Yang , L. 2010 . ‘Spline-Backfitted Kernel Smoothing of Additive Coefficient Model’ . Econometric Theory , 26 : 29 – 59 .
   Web of Science ®Google Scholar
• Ma , S. and Yang , L. 2011 . ‘Spline-Backfitted Kernel Smoothing of Partially Linear Additive Model’ . Journal of Statistical Planning and Inference , 141 : 204 – 219 .
   Web of Science ®Google Scholar
• Ma , S. , Yang , L. and Carroll , R. J. 2012 . ‘A Simultaneous Confidence Band for Sparse Longitudinal Data’ . Statistica Sinica , 22 : 95 – 122 .
   PubMed Web of Science ®Google Scholar
• Ramsay , J. O. and Silverman , B. W. 2005 . Functional Data Analysis , 2 , New York : Springer . Springer Series in Statistics
   Google Scholar
• Rice , J. A. and Wu , C. O. 2001 . ‘Nonparametric Mixed Effects Models for Unequally Sampled Noisy Curves’ . Biometrics , 57 : 253 – 259 .
   PubMed Web of Science ®Google Scholar
• Wang , J. and Yang , L. 2009a . ‘Polynomial Spline Confidence Bands for Regression Curves’ . Statistica Sinica , 19 : 325 – 342 .
   Web of Science ®Google Scholar
• Wang , L. and Yang , L. 2009b . ‘Spline Estimation of Single Index Model’ . Statistica Sinica , 19 : 765 – 783 .
   Web of Science ®Google Scholar
• Xue , L. and Yang , L. 2006 . ‘Additive Coefficient Modelling via Polynomial Spline’ . Statistica Sinica , 16 : 1423 – 1446 .
   Web of Science ®Google Scholar
• Yao , F. , Müller , H. G. and Wang , J. L. 2005 . ‘Functional Data Analysis for Sparse Longitudinal Data’ . Journal of the American Statistical Association , 100 : 577 – 590 .
   Web of Science ®Google Scholar
• Zhao , Z. and Wu , W. 2008 . ‘Confidence Bands in Nonparametric Time Series Regression’ . The Annals of Statistics , 36 : 1854 – 1878 .
   Web of Science ®Google Scholar
• Zhou , Z. and Wu , W. 2010 . ‘Simultaneous Inference of Linear Models with Time Varying Coefficients’ . Journal of the Royal Statistical Society. Series B , 72 : 513 – 531 .
   Google Scholar
• Zhou , S. , Shen , X. and Wolfe , D. A. 1998 . ‘Local Asymptotics of Regression Splines and Confidence Regions’ . The Annals of Statistics , 26 : 1760 – 1782 .
   Web of Science ®Google Scholar