2 Combined Phase-Amplitude fPCA
3 Functional Tolerance Bounds
4 Simulation Results
5 Applications to Real Data
6 Discussion and Future Work
-  A. Bhattacharya, On a measure of divergence between two statistical populations defined by their probability distributions, Bulletin of Calcutta Mathematical Society 35 (1943), pp. 99–109.
-  R. Bousseljot, D. Kreiseler, and A. Schnabel, Nutzung der EKG-signaldatenbank CAR-DIODAT der PTB uber das internet, Biomedizinische Technik 40 (1995), pp. S317–S318.
-  A.C. Davison and D.V. Hinkley, Bootsrap Methods and their Application, Cambridge University Press, 1997.
-  A.C. Davison, D.V. Hinkley, and G.A. Young, Recent developments in bootstrap methodology, Statistical Science 18 (2003), pp. 141–157.
-  F. Ferraty and P. Vieu, Nonparametric Functional Data Analysis: Theory and Practice, Springer-Verlag New York, Inc., 2006.
-  A.L. Goldberger, L.A.N. Amaral, L. Glass, J.M. Hausdorff, P.C. Ivanov, R.G. Mark, J.E. Mietus, G.B. Moody, C. Peng, and H.E. Stanley, Physiobank, physiotoolkit, and physionet: Components of a new research resource for complex physiologic signals., Circulation 101 (2000), pp. e215–e220. Available at http://www.physionet.org.
-  M. Grasso, A. Menafoglio, B.M. Colosimo, and P. Secchi, Using curve-registration information for profile monitoring, Journal of Quality Technology 48 (2016), pp. 99–127.
-  G.J. Hahn and W.Q. Meeker, Statistical Intervals: A Guide for Practitioners, John Wiley & Sons, Inc., 2011.
-  A. Kneip and J.O. Ramsay, Combining registration and fitting for functional models, Journal of the American Statistical Association 103 (2008).
-  K. Krishnamoorthy and T. Matthew, Statistical Tolerance Regions: Theory, Applications, and Computation, Wiley: New York, 2009.
K. Krishnamoorthy and S. Mondal,
Improved tolerance factors for multivariate normal distributions, Communications in Statistics - Simulation and Computation 35 (2006), pp. 461–478.
-  S. Kurtek, A geometric approach to pairwise Bayesian alignment of functional data using importance sampling, Electronic Journal of Statistics 11 (2017), pp. 502–531.
-  S. Kurtek and K. Bharath, Bayesian sensitivity analysis with Fisher–Rao metric, Biometrika 102 (2015), pp. 601–616.
-  S. Kurtek, A. Srivastava, and W. Wu, Signal Estimation Under Random Time-Warpings and Nonlinear Signal Alignment, in Proceedings of Neural Information Processing Systems (NIPS). 2011.
-  S. Kurtek, W. Wu, G.E. Christensen, and A. Srivastava, Segmentation, alignment and statistical analysis of biosignals with application to disease classification, Journal of Applied Statistics 40 (2013), pp. 1270–1288.
-  S. Lahiri, D. Robinson, and E. Klassen, Precise matching of PL curves in in the Square Root Velocity framework, Geometry, Imaging and Computing 2 (2015), pp. 133–186.
-  S. Lee and S. Jung, Combined analysis of amplitude and phase variations in functional data, arXiv:1603.01775 [stat.ME] (2017), pp. 1–21. Available at https://arxiv.org/abs/1603.01775.
-  J.R. Lewis, D. Brooks, and M.L. Benson, Methods for uncertainity quantification and comparison of weld residual stress measurements and predicitions, Proceedings of Pressure Vessels and Piping (2017).
-  Y. Lu, R. Herbei, and S. Kurtek, Bayesian registration of functions with a Gaussian process prior, Journal of Computational and Graphical Statistics DOI: 10.1080/10618600.2017.1336444 (2017).
-  A.H. Mahmoudi, S. Hossain, C.E. Truman, D.J. Smith, and M.J. Pavier, A new procedure to measure near yield residual stresses using the deep hole drilling technique, Experimental Mechanics 49 (2008), pp. 595–604.
-  J. Marron, J. Ramsay, L. Sangalli, and A. Srivastava, Functional data analysis of amplitude and phase variation, Statistical Science 30 (2015), pp. 468–484.
-  M.B. Prime, R.J. Sebring, J.M. Edwards, D.J. Hughes, and P.J. Webster, Laser surface-contouring and spline data-smoothing for residual-stress measuremen, Experimental Mechanics 44 (2004), pp. 176–184.
-  J.O. Ramsay and B.W. Silverman, Functional Data Analysis, Springer, 2005.
-  L.N. Rathnayake and P.K. Choudhary, Tolerance bands for functional data, Biometrics 72 (2016), pp. 503–512.
-  D. Robinson, Functional analysis and partial matching in the square root velocity framework, Ph.D. diss., Florida State University, 2012.
-  A. Srivastava and I.H. Jermyn, Looking for shapes in two-dimensional, cluttered point clouds, IEEE Trans. Pattern Analysis and Machine Intelligence 31 (2009), pp. 1616–1629.
-  A. Srivastava, E. Klassen, S. Joshi, and I. Jermyn, Shape analysis of elastic curves in Euclidean spaces, IEEE Trans. Pattern Analysis and Machine Intelligence 33 (2011), pp. 1415–1428.
-  A. Srivastava and E.P. Klassen, Functional and Shape Data Analysis, Springer-Verlag, 2016.
-  A. Srivastava, W. Wu, S. Kurtek, E. Klassen, and J.S. Marron, Registration of functional data using Fisher-Rao metric, arXiv:1103.3817v2 [math.ST] (2011). Available at http://arxiv.org/abs/1103.3817v2.
-  C.B. Storlie, M.L. Fugate, D.M. Higdon, A.V. Huzurbazar, E.G. Francois, and D.C. McHugh, Methods for characterizing and comparing populations of shock wave curves, Technometrics 55 (2013), pp. 436–449.
-  Y. Sun and M.G. Genton, Functional boxplots, Journal of Computational and Graphical Statistics 20 (2011), pp. 316–334.
-  J.D. Tucker, Functional statistical process control using elastic methods, Proceedings of Joint Statistical Meetings (2016).
-  J.D. Tucker, W. Wu, and A. Srivastava, Generative models for functional data using phase and amplitude separation, Computational Statistics and Data Analysis 61 (2013), pp. 50–66.
-  A. Veeraraghavan, A. Srivastava, A.K. Roy-Chowdhury, and R. Chellappa, Rate-invariant recognition of humans and their activities, IEEE Trans. on Image Processing 8 (2009), pp. 1326–1339.
-  W. Xie, S. Kurtek, K. Bharath, and Y. Sun, A geometric approach to visualization of variability in functional data, Journal of American Statistical Association 112 (2017), pp. 979–993.
-  Q. Yu, X. Lu, and J.S. Marron, Principal nested spheres for time-warped functional data analysis, Journal of Computational and Graphical Statistics 26 (2017), pp. 144–151.