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ARTICLES: Penalized Modeling for Regression and Classification

Functional Additive Mixed Models

Pages 477-501 | Received 01 Jul 2013, Published online: 16 Jun 2015

References

  • Abramovich, F., and Angelini, C. (2006), “Testing in Mixed-Effects FANOVA Models,” Journal of Statistical Planning and Inference, 136, 4326–4348.
  • Antoniadis, A., and Sapatinas, T. (2007), “Estimation and Inference in Functional Mixed-Effects Models,” Computational Statistics & Data Analysis, 51, 4793–4813.
  • Aston, J. A.D., Chiou, J.M., and Evans, J.P. (2010), “Linguistic Pitch Analysis Using Functional Principal Component Mixed Effect Models,” Journal of the Royal Statistical Society, Series C, 59, 297–317.
  • Baladandayuthapani, V., Mallick, B.K., Hong, M., Lupton, J.R., Turner, N.D., and Carroll, R.J. (2008), “Bayesian Hierarchical Spatially Correlated Functional Data Analysis With Application to Colon Carcinogenesis,” Biometrics, 64, 64–73.
  • Basser, P., Pajevic, S., Pierpaoli, C., and Duda, J. (2000), “In Vivo Fiber Tractography Using DT-MRI Data,” Magnetic Resonance in Medicine, 44, 625–632.
  • Bigelow, J.L., and Dunson, D.B. (2007), “Bayesian Adaptive Regression Splines for Hierarchical Data,” Biometrics, 63, 724–732.
  • Brumback, B., and Rice, J.A. (1998), “Smoothing Spline Models for the Analysis of Nested and Crossed Samples of Curves” (with discussion), Journal of the American Statistical Association, 93, 961–994.
  • Brumback, B., Ruppert, D., and Wand, M.P. (1999), “Comment,” Journal of the American Statistical Association, 94, 794–797.
  • Chen, K., and Müller, H.-G. (2012), “Modeling Repeated Functional Observations,” Journal of the American Statistical Association, 107, 1599–1609.
  • Chiou, J., Müller, H., and Wang, J. (2004), “Functional Response Models,” Statistica Sinica, 14, 675–694.
  • Crainiceanu, C.M., Reiss, P. T. (coordinating authors), Goldsmith, J., Greven, S., Huang, L., and Scheipl, F. (Contributors) (2011), Refund: Regression With Functional Data, R package version 0.1-5.
  • Crainiceanu, C.M., and Ruppert, D. (2004), “Likelihood Ratio Tests in Linear Mixed Models With One Variance Component,” Journal of the Royal Statistical Society, Series B, 66, 165–185.
  • Crainiceanu, C.M., Ruppert, D., Claeskens, G., and Wand, M.P. (2005), “Exact Likelihood Ratio Tests for Penalised Splines,” Biometrika, 92, 91–103.
  • Currie, I.D., Durban, M., and Eilers, P. H.C. (2006), “Generalized Linear Array Models With Applications to Multidimensional Smoothing,” Journal of the Royal Statistical Society, Series B, 68, 259–280.
  • De Boor, C. (1978), A Practical Guide to Splines, New York: Springer.
  • Delicado, P., Giraldo, R., Comas, C., and Mateu, J. (2010), “Statistics for Spatial Functional Data: Some Recent Contributions,” Environmetrics, 21, 224–239.
  • Di, C.Z., Crainiceanu, C.M., Caffo, B.S., and Punjabi, N.M. (2009), “Multilevel Functional Principal Component Analysis,” Annals of Applied Statistics, 3, 458–488.
  • Fang, Y., Liu, B., Müller, H.-G., and Wang, J.-L. (2013), PACE: Principal Analysis by Conditional Expectation, Version 2.16.
  • Faraway, J.J. (1997), “Regression Analysis for a Functional Response,” Technometrics, 39, 254–261.
  • Febrero-Bande, M., and de la Fuente, M. (2012), “Statistical Computing in Functional Data Analysis: The R package fda.usc,” Journal of Statistical Software, 51, 1–28.
  • Ferraty, F., Goia, A., Salinelli, E., and Vieu, P. (2011), “Recent Advances on Functional Additive Regression,” in Recent Advances in Functional Data Analysis and Related Topics, ed. F. Ferraty, New York: Springer, pp. 97–102.
  • Ferraty, F., and Vieu, P. (2006), Nonparametric Functional Data Analysis: Theory and Practice, New York: Springer.
  • Giraldo, R., Delicado, P., and Mateu, J. (2010), “Continuous Time-Varying Kriging for Spatial Prediction of Functional Data: An Environmental Application,” Journal of Agricultural, Biological, and Environmental Statistics, 15, 66–82.
  • Goldsmith, J., Bobb, J., Crainiceanu, C.M., Caffo, B., and Reich, D. (2011), “Penalized Functional Regression,” Journal of Computational and Graphical Statistics, 20, 830–851.
  • Goldsmith, J., Crainiceanu, C.M., Caffo, B., and Reich, D. (2012), “Longitudinal Penalized Functional Regression for Cognitive Outcomes on Neuronal Tract Measurements,” Journal of the Royal Statistical Society, 61, 453–469.
  • Goldsmith, J., Greven, S., and Crainiceanu, C.M. (2013), “Corrected Confidence Bands for Functional Data Using Principal Components,” Biometrics, 69, 41–51.
  • Greven, S., Crainiceanu, C.M., Caffo, B.S., and Reich, D. (2010), “Longitudinal Functional Principal Component Analysis,” Electronic Journal of Statistics, 4, 1022–1054.
  • Greven, S., Crainiceanu, C.M., Küchenhoff, H., and Peters, A. (2008), “Restricted Likelihood Ratio Testing for Zero Variance Components in Linear Mixed Models,” Journal of Computational and Graphical Statistics, 17, 870–891.
  • Greven, S., and Kneib, T. (2010), “On the Behaviour of Marginal and Conditional Aic in Linear Mixed Models,” Biometrika, 97, 773–789.
  • Gromenko, O., Kokoszka, P., Zhu, L., and Sojka, J. (2012), “Estimation and Testing for Spatially Indexed Curves With Application to Ionospheric and Magnetic Field Trends,” The Annals of Applied Statistics, 6, 669–696.
  • Guo, W. (2002), “Functional Mixed Effects Models,” Biometrics, 58, 121–128.
  • He, G., Müller, H.-G., and Wang, J.L. (2000), “Extending Correlation and Regression From Multivariate to Functional Data,” in Asymptotics in Statistics and Probability, ed. M. Puri, Utrecht: VSP International Science Publishers, pp. 301–315.
  • Herrick, R. (2013), WFMM, (Version 3.0 ed.). Anderson Cancer Center, The University of Texas M.D.
  • Hörmann, S., and Kokoszka, P. (2010), “Weakly Dependent Functional Data,” The Annals of Statistics, 38, 1845–1884.
  • Hörmann, S. (2011), “Consistency of the Mean and the Principal Components of Spatially Distributed Functional Data,” in Recent Advances in Functional Data Analysis and Related Topics, ed. F. Ferraty, New York: Springer, pp. 169–175.
  • Ivanescu, A.E., Staicu, A.-M., Scheipl, F., and Greven, S. (2012), “Penalized Function-on-Function Regression,” Technical Report 254, Johns Hopkins University, Department of Biostatistics Working Papers.
  • James, G.M. (2002), “Generalized Linear Models With Functional Predictors,” Journal of the Royal Statistical Society, Series B, 64, 411–432.
  • Krafty, R.T., Hall, M., and Guo, W. (2011), “Functional Mixed Effects Spectral Analysis,” Biometrika, 98, 583–598.
  • Krivobokova, T., and Kauermann, G. (2007), “A Note on Penalized Spline Smoothing With Correlated Errors,” Journal of the American Statistical Association, 102, 1328–1337.
  • Li, Y., Wang, N., Hong, M., Turner, N.D., Lupton, J.R., and Carroll, R.J. (2007), “Nonparametric Estimation of Correlation Functions in Longitudinal and Spatial Data, With Application to Colon Carcinogenesis Experiments,” The Annals of Statistics, 35, 1608–1643.
  • Malfait, N., and Ramsay, J. (2003), “The Historical Functional Linear Model,” Canadian Journal of Statistics, 31, 115–128.
  • Marra, G., and Wood, S.N. (2011), “Practical Variable Selection for Generalized Additive Models,” Computational Statistics & Data Analysis, 55, 2372–2387.
  • Marra, G., and Wood, S.N. (2012), “Coverage Properties of Confidence Intervals for Generalized Additive Model Components,” Scandinavian Journal of Statistics, 39, 53–74.
  • McLean, M.W., Hooker, G., Staicu, A.-M., Scheipl, F., and Ruppert, D. (2014), “Functional Generalized Additive Models,” Journal of Computational and Graphical Statistics, 23, 249–269.
  • Morris, J.S., and Carroll, R.J. (2006), “Wavelet-Based Functional Mixed Models,” Journal of the Royal Statistical Society, Series B, 68, 179–199.
  • Morris, J.S., Vannucci, M., Brown, P.J., and Carroll, R.J. (2003), “Wavelet-Based Nonparametric Modeling of Hierarchical Functions in Colon Carcinogenesis,” Journal of the American Statistical Association, 98, 573–583.
  • Müller, H.-G., and Yao, F. (2008), “Functional Additive Models,” Journal of the American Statistical Association, 103, 1534–1544.
  • Nerini, D., Monestiez, P., and Manté, C. (2010), “Cokriging for Spatial Functional Data,” Journal of Multivariate Analysis, 101, 409–418.
  • Nychka, D. (1988), “Confidence Intervals for Smoothing Splines,” Journal of the American Statistical Association, 83, 1134–1143.
  • Panaretos, V.M., and Tavakoli, S. (2013a), “Cramér-Karhunen-Loève Representation and Harmonic Principal Component Analysis of Functional Time Series,” Stochastic Processes and their Applications, 123, 2279–2807.
  • Panaretos, V.M., and Tavakoli, S. (2013b), “Fourier Analysis of Stationary Time Series in Function Space,” The Annals of Statistics, 41, 568–603.
  • Prchal, L., and Sarda, P. (2007), “Spline Estimator for Functional Linear Regression With Functional Response,” unpublished.
  • Qin, L., and Guo, W. (2006), “Functional Mixed-Effects Model for Periodic Data,” Biostatistics, 7, 225–234.
  • Ramsay, J.O., Wickham, H., Graves, S., and Hooker, G. (2011), Fda: Functional Data Analysis, R package version 2.2.7.
  • R Development Core Team. (2011), R: A Language and Environment for Statistical Computing, Vienna, Austria: R Foundation for Statistical Computing.
  • Reiss, P.T., Huang, L., and Mennes, M. (2010), “Fast Function-on-Scalar Regression With Penalized Basis Expansions,” The International Journal of Biostatistics, 6, 28.
  • Reiss, P.T., and Ogden, T. (2007), “Functional Principal Component Regression and Functional Partial Least Squares,” Journal of the American Statistical Association, 102, 984–996.
  • Reiss, P.T., and Ogden, T. (2009), “Smoothing Parameter Selection for a Class of Semiparametric Linear Models,” Journal of the Royal Statistical Society, Series B, 71, 505–523.
  • Ruppert, D., Carroll, R.J., and Wand, M.P. (2003), Semiparametric Regression, Cambridge, UK: Cambridge University Press.
  • Scarpa, B., and Dunson, D.B. (2009), “Bayesian Hierarchical Functional Data Analysis via Contaminated Informative Priors,” Biometrics, 65, 772–780.
  • Scheipl, F., and Greven, S. (2012), “Identifiability in Penalized Function-on-Function Regression Models,” Technical Report 125, LMU München.
  • Scheipl, F., Greven, S., and Küchenhoff, H. (2008), “Size and Power of Tests for a Zero Random Effect Variance or Polynomial Regression in Additive and Linear Mixed Models,” Computational Statistics & Data Analysis, 52, 3283–3299.
  • Staicu, A.-M., Crainiceanu, C.M., and Carroll, R.J. (2010), “Fast Methods for Spatially Correlated Multilevel Functional Data,” Biostatistics, 11, 177–194.
  • Staicu, A.-M., Crainiceanu, C.M., Ruppert, D., and Reich, D. (2011), “Modeling Functional Data With Spatially Heterogeneous Shape Characteristics,” Biometrics, 68, 331–343.
  • Wood, S.N. (2004), “Stable and Efficient Multiple Smoothing Parameter Estimation for Generalized Additive Models,” Journal of the American Statistical Association, 99, 673–686.
  • Wood, S.N. (2006), Generalized Additive Models: An Introduction With R, London, UK: Chapman & Hall/CRC.
  • Wood, S.N. (2011), “Fast Stable Restricted Maximum Likelihood and Marginal Likelihood Estimation of Semiparametric Generalized Linear Models,” Journal of the Royal Statistical Society, Series B, 73, 3–36.
  • Wood, S.N. (2013), “On p-Values for Smooth Components of an Extended Generalized Additive Model,” Biometrika, 100, 221–228.
  • Wood, S.N., Scheipl, F., and Faraway, J.J. (2013), “Straightforward Intermediate Rank Tensor Product Smoothing in Mixed Models,” Statistics and Computing, 23, 341–360.
  • Wu, Y., Fan, J., and Müller, H.-G. (2010), “Varying-Coefficient Functional Linear Regression,” Bernoulli, 16, 730–758.
  • 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.
  • Zhou, L., Huang, J.Z., Martinez, J.G., Maity, A., Baladandayuthapani, V., and Carroll, R.J. (2010), “Reduced Rank Mixed Effects Models for Spatially Correlated Hierarchical Functional Data,” Journal of the American Statistical Association, 105, 390–400.
  • Zhu, H., Brown, P.J., and Morris, J.S. (2011), “Robust, Adaptive Functional Regression in Functional Mixed Model Framework,” Journal of the American Statistical Association, 106, 1167–1179.

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