1,320
Views
21
CrossRef citations to date
0
Altmetric
Theory and Methods

Principal Flows

Pages 424-436 | Received 01 Dec 2012, Published online: 19 Mar 2014

REFERENCES

  • Bhattacharya, R., Patrangenaru, V. (2003), Large Sample Theory of Intrinsic and Extrinsic Sample Means on Manifolds. I, The Annals of Statistics, 31, 1–29.
  • Bhattacharya, R., Patrangenaru, V. (2005), Large Sample Theory of Intrinsic and Extrinsic Sample Means on Manifolds. II, The Annals of Statistics, 33, 1225–1259.
  • Brillinger, D.R. (1997), A Particle Migrating Randomly on the Sphere, Journal of Theoretical Probability, 10, 429–443.
  • Chaudhuri, P., Marron, J.S. (2000), Scale Space View of Curve Estimation, The Annals of Statistics, 28, 408–428.
  • Dryden, I.L., Koloydenko, A., Zhou, D. (2009), Non-Euclidean Statistics for Covariance Matrices, With Applications to Diffusion Tensor Imaging, Annals of Applied Statistics, 3, 1102–1123.
  • Dryden, I.L., and Mardia, K.V. (1998), Statistical Shape Analysis, New York: Wiley.
  • Fletcher, P.T., Joshi, S. (2007), Riemannian Geometry for the Statistical Analysis of Diffusion Tensor Data, Signal Processing, 87, 250–262.
  • Fletcher, P.T., Lu, C. Pizer, Joshi, S. (2004), Principal Geodesic Analysis for the Study of Nonlinear Statistics of Shape, IEEE Transactions on Medical Imaging, 23, 995–1005.
  • Fréchet, M. (1948), Les éléments Aléatoires de Nature Quelconque Dans un Espace Distancié, Annales de l’Institut Henri Poincaré, 10, 215–310.
  • Goodall, C.R. (1991), “Procrustes Methods in the Statistical Analysis of Shape” (with discussion), Journal of the Royal Statistical Society, Series B, 53, 285–339.
  • Hastie, T., Stuetzle, W. (1989), Principal Curves, Journal of the American Statistical Association, 84, 502–516.
  • Huckemann, S., Hotz, T., Munk, A. (2010), “Intrinsic Shape Analysis: Geodesic PCA for Riemannian Manifolds Modulo Isometric Lie Group Actions” (with discussion), Statistica Sinica, 20, 1–100.
  • Huckemann, S., Ziezold, H. (2006), Principal Component Analysis for Riemannian Manifolds, With an Application to Triangular Shape Spaces, Advances in Applied Probability, 38, 299–319.
  • Jupp, P.E., Kent, J.T. (1987), Fitting Smooth Paths to Spherical Data, Journal of the Royal Statistical Soceity, Series C, 36, 34–46.
  • Jung, S., Foskey, M., Marron, J.S. (2010), Principal arc Analysis on Direct Product Manifolds, Annals of Applied Statistics, 5, 578–603.
  • Jung, S., Dryden, I.L., Marron, J.S. (2012), Analysis of Principal Nested Spheres, Biometrika, 99, 551–568.
  • Karcher, H. (1977), Riemannian Center of Mass and Mollifier Smoothing, Communications in Pure Applied Mathematics, 30, 509–541.
  • Kendall, D.G., Barden, D., Carne, T.K., and H. Le, (1999), Shape and Shape Theory, New York: Wiley.
  • Kendall, W.S., Le, H. (2011), Limit Theorems for Empirical Fréchet Means of Independent and Non-Identically Distributed Manifold-Valued Random Variables, Brazilian Journal of Probability and Statistics, 25, 323–352.
  • Kenobi, K., Dryden, I.L., Le, H. (2010), Shape Curves and Geodesic Modelling, Biometrika, 97, 567–584.
  • Kume, A., Dryden, I.L., Le, H. (2007), Shape-Space Smoothing Splines for Planar Landmark Data, Biometrika, 94, 513–528.
  • Magnus, J.R. (1985), On Differentiating Eigenvalues and Eigenvectors, Econometric Theory, 1, 179–191.
  • Mardia, K.V., and Jupp, P.E. (2000), Directional Statistics, Chichester: Wiley.
  • Mardia, K.V., Khatri, C.G. (1977), Uniform Distribution on a Stiefel Manifold, Journal of Multivariate Analysis, 7, 468–473.
  • Rabier, P.J., Rheinboldt, W.C. (1995), On the Numerical Solution of the Euler-Lagrange Equations, SIAM Journal on Numerical Analysis, 32, 318–329.
  • Schmidt-Hieber, J., Munk, A., Dümbgen, L. (2013), Multiscale Methods for Shape Constraints in Deconvolution: Confidence Statements for Qualitative Features, The Annals of Statistics, 41, 1299–1328.
  • Schwartzman, A. (2006), Random Ellipsoids and False Discovery Rates: Statistics for Diffusion Tensor Imaging Data, Ph.D. Thesis, Stanford University.
  • Small, C.G. (1996), The Statistical Theory of Shape, New York: Springer.
  • Stoyan, D., Kendall, W.S., and Mecke, J. (1995), Stochastic Geometry and Its Applications, Chichester: Wiley.
  • Su, J., Dryden, I.L., Klassen, E., Le, H., Srivastava, A. (2012), Fitting Smoothing Splines to Time-Indexed, Noisy Points on Nonlinear Manifolds, Image and Vision Computing, 30, 428–442.
  • Thorpe, J. (1979), Elementary Topics in Differential Geometry, New York: Springer-Verlag.
  • U.S. Geological Survey, Global Earthquake Search. . Available at: http://earthquake.usgs.gov/earthquakes/eqarchives/epic/, in progress.
  • Watson, G.S. (1983), Statistics on Spheres, New York: Wiley.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.