Copula Gaussian Graphical Models for Functional Data

References

• Bach, F. R. (2008), “Consistency of the Group Lasso and Multiple Kernel Learning,” The Journal of Machine Learning Research , 9, 1179–1225.
   Web of Science ®Google Scholar
• Baker, C. R. (1973), “Joint Measures and Cross-Covariance Operators,” Transactions of The American Mathematical Society , 186, 273–289.
   Web of Science ®Google Scholar
• Bosq, D. (2000), Linear Process in Function Spaces: Theory and Application, Lecture Notes in Statistics (Vol. 149), New York: Springer.
   Google Scholar
• Cheng, R. , and Herskovits, E. H. (2007), “Graphical-Model-Based Multivariate Analysis of Functional Magnetic-Resonance Data,” NeuroImage , 35, 635–647. DOI: https://doi.org/10.1016/j.neuroimage.2006.11.040.
   PubMed Web of Science ®Google Scholar
• Chiou, J.-M. , Chen, Y.-T. , and Yang, Y.-F. (2014), “Multivariate Functional Principal Component Analysis: A Normalization Approach,” Statistica Sinica , 24, 1571–1596.
   Web of Science ®Google Scholar
• Darroch, J. N. , Lauritzen, S. L. , and Speed, T. P. (1980), “Markov Fields and Log Linear Models for Contingency Tables,” The Annals of Statistics , 8, 522–539.
   Web of Science ®Google Scholar
• Dawid, A. P. , and Lauritzen, S. L. (1993), “Hyper Markov Laws in the Statistical Analysis of Decomposable Graphical Models,” The Annals of Statistics , 21, 1272–1317.
   Web of Science ®Google Scholar
• Ferraty, F. , and Vieu, P. (2006), Nonparametric Functional Data Analysis: Theory and Practice , New York: Springer.
   Google Scholar
• Gu, Q. , Cao, Y. , Ning, Y. , and Liu, H. (2015), “Local and Global Inference for High Dimensional Nonparanormal Graphical Models,” arXiv no. 1502.02347.
   Google Scholar
• Horváth, L. , and Kokoszka, P. (2012), Inference for Functional Data With Applications (Vol. 200), New York: Springer.
   Google Scholar
• Hsing, T. , and Eubank, R. (2015), Theoretical Foundations of Functional Data Analysis, With an Introduction to Linear Operators , New York: Wiley.
   Google Scholar
• Ingber, L. (1997), “Statistical Mechanics of Neocortical Interactions: Canonical Momenta Indicators of Electroencephalography,” Physical Review E , 55, 4578.
   Web of Science ®Google Scholar
• Kendall, M. G. (1948), Rank Correlation Methods , London: Charles Griffin and Co. Ltd.
   Google Scholar
• Kruskal, W. H. (1958), “Ordinal Measures of Association,” Journal of the American Statistical Association , 53, 814–861.
   Web of Science ®Google Scholar
• Lauritzen, S. L. (1996), Graphical Models , Oxford: Clarendon Press.
   Google Scholar
• Lauritzen, S. L. , Speed, T. P. , and Vijayan, K. (1984), “Decomposable Graphs and Hypergraphs,” Journal of the Australian Mathematical Society, Series A, 36, 12–29.
   Google Scholar
• Lazar, N. A. , Lura, B. , Sweeney, J. A. , and Eddy, W. F. (2002), “Combining Brains: A Survey of Methods for Statistical Pooling of Information,” NeuroImage , 16, 538–550. DOI: https://doi.org/10.1006/nimg.2002.1107.
   PubMed Web of Science ®Google Scholar
• Li, B. (2018), “Linear Operator-Based Statistical Analysis: A Useful Paradigm for Big Data,” The Canadian Journal of Statistics , 46, 79–103.
   Web of Science ®Google Scholar
• Li, B. , and Babu, J. (2019), A Graduate Course on Statistical Inference , New York: Springer.
   Google Scholar
• Li, B. , Chun, H. , and Zhao, H. (2014), “On an Additive Semigraphoid Model for Statistical Networks With Application to Pathway Analysis,” Journal of the American Statistical Association , 109, 1188–1204. DOI: https://doi.org/10.1080/01621459.2014.882842.
   PubMed Web of Science ®Google Scholar
• Li, B. , Kim, M. K. , and Altman, N. (2010), “On Dimension Folding of Matrix-or Array-Valued Statistical Objects,” The Annals of Statistics , 1094–1121.
   Web of Science ®Google Scholar
• Li, B. , and Solea, E. (2018), “A Nonparametric Graphical Model for Functional Data With Application to Brain Networks Based on fMRI,” Journal of the American Statistical Association , 113, 1637–1655.
   Web of Science ®Google Scholar
• Li, B. , and Song, J. (2017), “Nonlinear Sufficient Dimension Reduction for Functional Data,” The Annals of Statistics , 45, 1059–1095.
   Web of Science ®Google Scholar
• Liu, H. , Han, F. , Yuan, M. , Lafferty, J. , and Wasserman, L. (2012), “The Nonparanormal Skeptic,” arXiv no. 1206.6488.
   Google Scholar
• Liu, H. , Lafferty, J. , and Wasserman, L. (2009), “The Nonparanormal: Semiparametric Estimation of High Dimensional Undirected Graphs,” The Journal of Machine Learning Research , 10, 2295–2328.
   Web of Science ®Google Scholar
• Meinshausen, N. , and Bühlmann, P. (2006), “High-Dimensional Graphs With the Lasso,” The Annals of Statistics , 34, 1436–1462.
   Web of Science ®Google Scholar
• Qiao, X. , Guo, S. , and James, G. M. (2019), “Functional Graphical Models,” Journal of the American Statistical Association , 114, 211–222.
   Web of Science ®Google Scholar
• Qiao, X. , Qian, C. , James, G. M. , and Guo, S. (2020), “Doubly Functional Graphical Models in High Dimensions,” Biometrika , 107, 415–431.
   Web of Science ®Google Scholar
• Ramsay, J. O. , and Silverman, B. W. (2005), Functional Data Analysis , New York: Springer.
   Google Scholar
• Wermuth, N. , and Lauritzen, S. L. (1983), “Graphical and Recursive Models for Contingency Tables,” Biometrika , 70, 537–552.
   Web of Science ®Google Scholar
• Wermuth, N. , and Lauritzen, S. L. (1990), “On Substantive Research Hypotheses, Conditional Independence Graphs and Graphical Chain Models” (with discussion), Journal of the Royal Statistical Society, Series B, 52, 21–72.
   Google Scholar
• Whittaker, J. (1990), Graphical Models in Applied Multivariate Statistics , Chichester: Wiley.
   Google Scholar
• Xue, L. , and Zou, H. (2012), “Regularized Rank-Based Estimation of High-Dimensional Nonparanormal Graphical Models,” The Annals of Statistics , 40, 2541–2571.
   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
• Yuan, M. , and Lin, Y. (2007), “Model Selection and Estimation in Gaussian Graphical Model,” Biometrika , 94, 19–35.
   Web of Science ®Google Scholar
• Zhang, X. L. , Begleiter, H. , Porjesz, B. , Wang, W. , and Litke, A. (1995), “Event Related Potentials During Object Recognition Tasks,” Brain Research Bulletin , 38, 531–538.
   PubMed Web of Science ®Google Scholar
• Zhu, H. , Strawn, N. , and Dunson, D. B. (2016), “Bayesian Graphical Models for Multivariate Functional Data,” Journal of Machine Learning Research , 17, 1–7.
   Web of Science ®Google Scholar