PROFIT: projection-based test in longitudinal functional data

References

• Baladandayuthapani, V., Mallick, B.K., Young 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.
   PubMed Web of Science ®Google Scholar
• Basser, P.J., and Pierpaoli, C. (2011), ‘Microstructural and Physiological Features of Tissues Elucidated by Quantitative-diffusion-tensor Mri’, Journal of Magnetic Resonance, 213, 560–570.
   PubMedGoogle Scholar
• Carroll, C., Gajardo, A., Chen, Y., Dai, X., Fan, J., Hadjipantelis, P.Z., Han, K., Ji, H., Mueller, H.-G., and Wang, J.-L. (2021), fdapace: Functional Data Analysis and Empirical Dynamics. R package version 0.5.6.
   Google Scholar
• Chen, K., Delicado Useros, P.F., and Müller, H.-G. (2017), ‘Modelling Function-valued Stochastic Processes, with Applications to Fertility Dynamics’, Journal of the Royal Statistical Society. Series B, Statistical Methodology, 79, 177–196.
   Web of Science ®Google Scholar
• Chen, X., and Fan, Y. (1999), ‘Consistent Hypothesis Testing in Semiparametric and Nonparametric Models for Econometric Time Series’, Journal of Econometrics, 91, 373–401.
   Web of Science ®Google Scholar
• Chen, K., and Müller, H.-G. (2012), ‘Modeling Repeated Functional Observations’, Journal of the American Statistical Association, 107, 1599–1609.
   Web of Science ®Google Scholar
• Ciccarelli, O., Werring, D.J., Barker, G.J., Griffin, C.M., Wheeler-Kingshott, C.A., Miller, D.H., and Thompson, A.J. (2003), ‘A Study of the Mechanisms of Normal-appearing White Matter Damage in Multiple Sclerosis Using Diffusion Tensor Imaging’, Journal of Neurology, 250, 287–292.
   PubMed Web of Science ®Google Scholar
• Coote, S., Garrett, M., Hogan, N., Larkin, A., and Saunders, J. (2009), ‘Getting the Balance Right: a Randomised Controlled Trial of Physiotherapy and Exercise Interventions for Ambulatory People with Multiple Sclerosis’, BMC Neurology, 9, 1–8.
   PubMed Web of Science ®Google Scholar
• 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.
   Google Scholar
• Crainiceanu, C., Ruppert, D., Claeskens, G., and Wand, M.P. (2005), ‘Exact Likelihood Ratio Tests for Penalised Splines’, Biometrika, 92, 91–103.
   Web of Science ®Google Scholar
• Cuesta-Albertos, J., and Febrero-Bande, M. (2010), ‘A Simple Multiway Anova for Functional Data’, Test, 19, 537–557.
   Web of Science ®Google Scholar
• Delgado, M.S., Henderson, D.J., and Parmeter, C.F. (2014), ‘Does Education Matter for Economic Growth?’ Oxford Bulletin of Economics and Statistics, 76, 334–359.
   Web of Science ®Google Scholar
• Di, C.-Z., Crainiceanu, C.M., Caffo, B.S., and Punjabi, N.M. (2009), ‘Multilevel Functional Principal Component Analysis’, The Annals of Applied Statistics, 3, 458.
   PubMed Web of Science ®Google Scholar
• Fan, Y., and Li, Q. (2000), ‘Consistent Model Specification Tests: Kernel-based Tests Versus Bierens’ ICM Tests’, Econometric Theory, 16, 1016–1041.
   Web of Science ®Google Scholar
• 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.
   PubMed Web of Science ®Google Scholar
• Goldsmith, J., Scheipl, F., Huang, L., Wrobel, J., Di, C., Gellar, J., Harezlak, J., McLean, M.W., Swihart, B., Xiao, L., Crainiceanu, C., and Reiss, P.T. (2020), refund: Regression with Functional Data. R package version 0.1-23.
   Google Scholar
• Greven, S., and Crainiceanu, C.M. (2013), ‘On Likelihood Ratio Testing for Penalized Splines’, AStA Advances in Statistical Analysis, 97, 387–402.
   Web of Science ®Google Scholar
• Greven, S., Crainiceanu, C., Caffo, B., and Reich, D. (2011), ‘Longitudinal Functional Principal Component Analysis’, in Recent Advances in Functional Data Analysis and Related Topics, Springer, New York, pp. 149–154.
   Google Scholar
• Guo, J., Zhou, B., and Zhang, J.-T. (2019), ‘New Tests for Equality of Several Covariance Functions for Functional Data’, Journal of the American Statistical Association, 114, 1251–1263.
   Web of Science ®Google Scholar
• Hall, P., Li, Q., and Racine, J.S. (2007), ‘Nonparametric Estimation of Regression Functions in the Presence of Irrelevant Regressors’, The Review of Economics and Statistics, 89, 784–789.
   Web of Science ®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
• Hasan, K.M., Gupta, R.K., Santos, R.M., Wolinsky, J.S., and Narayana, P.A. (2005), ‘Diffusion Tensor Fractional Anisotropy of the Normal-appearing Seven Segments of the Corpus Callosum in Healthy Adults and Relapsing-remitting Multiple Sclerosis Patients’, Journal of Magnetic Resonance Imaging: An Official Journal of the International Society for Magnetic Resonance in Medicine, 21, 735–743.
   PubMed Web of Science ®Google Scholar
• Hasenstab, K., Scheffler, A., Telesca, D., Sugar, C.A., Jeste, S., DiStefano, C., and Şentürk, D. (2017), ‘A Multi-dimensional Functional Principal Components Analysis of EEG Data’, Biometrics, 73, 999–1009.
   PubMed Web of Science ®Google Scholar
• Horváth, L., and Rice, G. (2015), ‘An Introduction to Functional Data Analysis and a Principal Component Approach for Testing the Equality of Mean Curves’, Revista Matemática Complutense, 28, 505–548.
   Web of Science ®Google Scholar
• Landau, H., and Shepp, L.A. (1970), ‘On the Supremum of a Gaussian Process’, Sankhyā: The Indian Journal of Statistics, Series A, 32, 369–378.
   Google Scholar
• Li, Y., and Hsing, T. (2010), ‘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
• Lynch, B., and Chen, K. (2018), ‘A Test of Weak Separability for Multi-way Functional Data, with Application to Brain Connectivity Studies’, Biometrika, 105, 815–831.
   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: Statistical Methodology, 68, 179–199.
   PubMed Web of Science ®Google Scholar
• Paparoditis, E., and Sapatinas, T. (2016), ‘Bootstrap-based Testing of Equality of Mean Functions or Equality of Covariance Operators for Functional Data’, Biometrika, 103, 727–733.
   Web of Science ®Google Scholar
• Park, S.Y., and Staicu, A.-M. (2015), ‘Longitudinal Functional Data Analysis’, Stat, 4, 212–226.
   PubMed Web of Science ®Google Scholar
• Park, S.Y., Staicu, A.-M., Xiao, L., and Crainiceanu, C.M. (2018), ‘Simple Fixed-effects Inference for Complex Functional Models’, Biostatistics, 19, 137–152.
   PubMed Web of Science ®Google Scholar
• Pinheiro, J., Bates, D., DebRoy, S., and Sarkar, D., and R Core Team (2021), nlme: Linear and Nonlinear Mixed Effects Models. R package version 3.1-152.
   Google Scholar
• Pomann, G.-M., Staicu, A.-M., and Ghosh, S. (2016), ‘A Two Sample Distribution-free Test for Functional Data with Application to a Diffusion Tensor Imaging Study of Multiple Sclerosis’, Journal of the Royal Statistical Society. Series C, Applied Statistics, 65, 395–414.
   PubMed Web of Science ®Google Scholar
• Ruppert, D., Wand, M.P., and Carroll, R.J. (2003), Semiparametric Regression (Vol. 12), Cambridge UK: Cambridge University Press.
   Google Scholar
• Scheffler, A., Telesca, D., Li, Q., Sugar, C.A., Distefano, C., Jeste, S., and Şentürk, D. (2020), ‘Hybrid Principal Components Analysis for Region-referenced Longitudinal Functional Eeg Data’, Biostatistics, 21, 139–157.
   PubMed Web of Science ®Google Scholar
• Scheipl, F., Greven, S., and Kuechenhoff, 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.
   Web of Science ®Google Scholar
• Scheipl, F., Staicu, A.-M., and Greven, S. (2015), ‘Functional Additive Mixed Models’, Journal of Computational and Graphical Statistics, 24, 477–501.
   PubMed Web of Science ®Google Scholar
• Shen, Q., and Faraway, J. (2004), ‘An F Test for Linear Models with Functional Responses’, Statistica Sinica, 1, 1239–1257.
   Google Scholar
• Staicu, A.-M., Islam, M.N., Dumitru, R., and Heugten, E. v. (2020), ‘Longitudinal Dynamic Functional Regression’, Journal of the Royal Statistical Society: Series C (Applied Statistics), 69, 25–46.
   PubMed Web of Science ®Google Scholar
• Staicu, A.-M., Li, Y., Crainiceanu, C.M., and Ruppert, D. (2014), ‘Likelihood Ratio Tests for Dependent Data with Applications to Longitudinal and Functional Data Analysis’, Scandinavian Journal of Statistics, 41, 932–949.
   Web of Science ®Google Scholar
• Wiencierz, A., Greven, S., and Küchenhoff, H. (2011), ‘Restricted Likelihood Ratio Testing in Linear Mixed Models with General Error Covariance Structure’, Electronic Journal of Statistics, 5, 1718–1734.
   Web of Science ®Google Scholar
• Wood, S.N. (2017), Generalized Additive Models: An Introduction with R, New York NY: CRC Press.
   Google Scholar
• Wynne, G., and Duncan, A.B. (2020), A kernel two-sample test for functional data. Preprint, arXiv:2008.11095.
   Google Scholar
• Xiao, L. (2019), ‘Asymptotic Theory of Penalized Splines’, Electronic Journal of Statistics, 13, 747–794.
   Web of Science ®Google Scholar
• Xiao, L. (2020), ‘Asymptotic Properties of Penalized Splines for Functional Data’, Bernoulli, 26, 2847–2875.
   Web of Science ®Google Scholar
• Xiao, L., Huang, L., Schrack, J.A., Ferrucci, L., Zipunnikov, V., and Crainiceanu, C.M. (2015), ‘Quantifying the Lifetime Circadian Rhythm of Physical Activity: a Covariate-dependent Functional Approach’, Biostatistics, 16, 352–367.
   PubMed Web of Science ®Google Scholar
• Xiao, L., Li, Y., and Ruppert, D. (2013), ‘Fast Bivariate P-splines: the Sandwich Smoother’, Journal of the Royal Statistical Society: Series B, 75, 577–599.
   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
• Yuan, Y., Gilmore, J.H., Geng, X., Martin, S., Chen, K., Wang, J.-l., and Zhu, H. (2014), ‘FMEM: Functional Mixed Effects Modeling for the Analysis of Longitudinal White Matter Tract Data’, NeuroImage, 84, 753–764.
   PubMed Web of Science ®Google Scholar
• Zhang, J.-T. (2011), ‘Statistical Inferences for Linear Models with Functional Responses’, Statistica Sinica, 21, 1431–1451.
   Web of Science ®Google Scholar
• Zhang, J.-T., and Chen, J. (2007), ‘Statistical Inferences for Functional Data’, The Annals of Statistics, 35, 1052–1079.
   Web of Science ®Google Scholar
• Zhang, J.-T., Cheng, M.-Y., Wu, H.-T., and Zhou, B. (2019), ‘A New Test for Functional One-way Anova with Applications to Ischemic Heart Screening’, Computational Statistics & Data Analysis, 132, 3–17.
   Web of Science ®Google Scholar
• Zhang, X., and Wang, J.-L. (2016), ‘From Sparse to Dense Functional Data and Beyond’, The Annals of Statistics, 44, 2281–2321.
   Web of Science ®Google Scholar