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Functional Data and Elastic Registration

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Functional and Shape Data Analysis

Part of the book series: Springer Series in Statistics ((SSS))

Abstract

Functional data analysis (FDA) is a branch of statistics where one observes, models, and analyzes quantities that are functions on certain intervals. This kind of data naturally arises in nearly every branch of science, ranging from engineering to geology, biology, medicine, and chemistry.

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References

  1. M. Adams, T. Ratiu, R. Schmid, The lie group structure of diffeomorphism groups and invertible fourier integral operators, with applications. In: Infinite-Dimensional Groups with Applications, ed. by V. Kac (Springer, New York, 1985)

    Google Scholar 

  2. S. Amari, Differential Geometric Methods in Statistics. Lecture Notes in Statistics, Vol. 28 (Springer, New York, 1985)

    Google Scholar 

  3. S. Amari, H. Nagaoka, Methods of Information Geometry, Mathematical Monographs Volume 191 (Oxford University Press, Oxford, 2000)

    Google Scholar 

  4. S.-I. Amari, O.E. Barndorff-Nielsen, R.E. Kass, S.L. Lauritzen, C.R. Rao, Differential Geometry in Statistical Inference, Monograph Series (Institute of Mathematical Statistics, Hayward, 1987)

    MATH  Google Scholar 

  5. A. Bhattacharya, On a measure of divergence between two statistical populations defined by their probability distributions. Bull. Calcutta Math. Soc. 35, 99–109 (1943)

    MathSciNet  Google Scholar 

  6. M. Bruveris, Optimal reparameterizations in square root velocity framework. arXiv, arXiv:1507.02728 (2015)

    Google Scholar 

  7. N.N. ÄŒencov, Statistical Decision Rules and Optimal Inferences, volume 53 of Translations of Mathematical Monographs (AMS, Providence, 1982)

    Google Scholar 

  8. D.G. Ebin, J. Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid. Ann. Math. Second Ser. 92 (1), 102–163 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  9. B. Efron, Defining the curvature of a statistical problem (with applications to second order efficiency). Ann. Stat. 3, 1189–1242 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  10. L. Horvath, P. Kkozska, Inference for Functional Data with Applications. Springer Series in Statistics (Springer, New York, 2012)

    Google Scholar 

  11. V.G. Kac, Infinite-Dimensional Lie Algebras, 3rd edn. (Cambridge University Press, Cambridge, 1990)

    Book  MATH  Google Scholar 

  12. R.E. Kass, P.W. Vos, Geometric Foundations of Asymptotic Inference (Wiley, London, 1997)

    Book  MATH  Google Scholar 

  13. A. Kneip, T. Gasser, Statistical tools to analyze data representing a sample of curves. Ann. Stat. 20, 1266–1305 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  14. S. Lahiri, D. Robinson, E. Klassen, Precise matching of PL curves in R N in square root velocity framework. Geom. Imaging Comput. 2 (3), 133–186 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  15. X. Leng, H.G. Mueller, Time ordering of gene coexpression. Biostatistics 7 (4), 569–584 (2006)

    Article  MATH  Google Scholar 

  16. X. Liu, H.G. Mueller, Functional convex averaging and synchronization for time-warped random curves. J. Am. Stat. Assoc. 99, 687–699 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  17. D.G. Luenberger, Optimization by Vector Space Methods (Wiley, New York, 1969)

    MATH  Google Scholar 

  18. J.O. Ramsay, X. Li, Curve registration. J. R. Stat. Soc. Ser. B 60, 351–363 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  19. J.O. Ramsay, B.W. Silverman, Functional Data Analysis, Second Edition. Springer Series in Statistics (Springer, New York, 2005)

    Google Scholar 

  20. C.R. Rao, Information and accuracy attainable in the estimation of statistical parameters. Bull. Calcutta Math. Soc. 37, 81–91 (1945)

    MathSciNet  MATH  Google Scholar 

  21. D. Robinson, Functional Analysis and Partial Matching in the Square Root Velocity Framework. PhD thesis, Florida State University, August 2012

    Google Scholar 

  22. A. Srivastava, E. Klassen, S.H. Joshi, I.H. Jermyn, Shape analysis of elastic curves in Euclidean spaces. IEEE Trans. PAMI 33, 1415–1428 (2011)

    Article  Google Scholar 

  23. A. Srivastava, W. Wu, S. Kurtek, E. Klassen, J.S. Marron, Registration of functional data using fisher-rao metric. arXiv, arXiv:1103.3817 (2011)

    Google Scholar 

  24. R. Tang, H.G. Mueller, Pairwise curve synchronization for functional data. Biometrika 95 (4), 875–889 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  25. P.W. Vosm, R.E. Kass, Geometrical Foundations of Asymptotic Inference (Wiley-Interscience, New York, 1997)

    Google Scholar 

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Srivastava, A., Klassen, E.P. (2016). Functional Data and Elastic Registration. In: Functional and Shape Data Analysis. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-4020-2_4

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