A Nonparametric Regression Model With Tree-Structured Response

REFERENCES

• Aydın , B. , Pataki , G. , Wang , H. , Bullitt , E. and Marron , J. 2009 . “A Principal Component Analysis for Trees,” . The Annals of Applied Statistics , 3 : 1597 – 1615 .
   Web of Science ®Google Scholar
• Aydın , B. , Pataki , G. , Wang , H. , Ladha , A. , Bullitt , E. and Marron , J. 2011 . “Visualizing the Structure of Large Trees,” . Electronic Journal of Statistics , 5 : 405 – 420 .
   Web of Science ®Google Scholar
• Aylward , S. and Bullitt , E. 2002 . “Initialization, Noise, Singularities, and Scale in Height Ridge Traversal for Tubular Object Centerline Extraction,” . IEEE Transactions on Medical Imaging , 21 ( 2 ) : 61 – 75 .
   PubMed Web of Science ®Google Scholar
• Banks , D. and Constantine , G. 1998 . “Metric Models for Random Graphs,” . Journal of Classification , 15 ( 2 ) : 199 – 223 .
   Web of Science ®Google Scholar
• Bhattacharya , R. and Patrangenaru , V. 2003 . “Large Sample Theory of Intrinsic and Extrinsic Sample Means on Manifolds. I,” . The Annals of Statistics , 31 : 1 – 29 .
   Web of Science ®Google Scholar
• Bhattacharya , R. 2005 . “Large Sample Theory of Intrinsic and Extrinsic Sample Means on Manifolds. II,” . The Annals of Statistics , 33 : 1225 – 1259 .
   Web of Science ®Google Scholar
• Bullitt , E. , Zeng , D. , Gerig , G. , Aylward , S. , Joshi , S. , Smith , J. , Lin , W. and Ewend , M. 2005 . “Vessel Tortuosity and Brain Tumor Malignancy: A Blinded Study,” . Academic Radiology , 12 : 1232 – 1240 .
   PubMed Web of Science ®Google Scholar
• Chaudhuri , P. and Marron , J. S. 1999 . “Sizer for Exploration of Structures in Curves,” . Journal of the American Statistical Association , 94 : 807 – 823 .
   Web of Science ®Google Scholar
• Marron , J. S. 2000 . “Scale Space View of Curve Estimation,” . The Annals of Statistics , 28 : 408 – 428 .
   Web of Science ®Google Scholar
• Chiu , S.-T. and Marron , J. S. 1990 . “The Negative Correlations Between Data-Determined Bandwidths and the Optimal Bandwidth,” . Statistics and Probability Letters , 10 : 173 – 180 .
   Web of Science ®Google Scholar
• Davis , B. 2008 . “Medical Image Analysis via Fréchet Means of Diffeomorphisms,” . Ph.D. dissertation, The University of North Carolina at Chapel Hill
   Google Scholar
• Davison , A. 2003 . Statistical Models , Cambridge : Cambridge University Press .
   Google Scholar
• Fletcher , P. T. , Lu , C. , Pizer , S. and Joshi , S. 2004 . “Principal Geodesic Analysis for the Study of Nonlinear Statistics of Shape,” . IEEE Transactions on Medical Imaging , 23 : 995 – 1005 .
   PubMed Web of Science ®Google Scholar
• Fréchet , M. 1948 . “Les Éléments Alétories de Nature Quelconque Dans un Espace Distancié,” . Annales de l’Institut Henri Poincaré , 10 : 215 – 310 .
   Google Scholar
• Härdle , W. 1990 . Applied Nonparametric Regression , Cambridge : Cambridge University Press .
   Google Scholar
• Härdle , W. , Hall , P. and Marron , J. 1988 . “How Far Are Automatically Chosen Regression Smoothing Parameters From Their Optimum?” . Journal of the American Statistical Association , 83 : 86 – 95 .
   Web of Science ®Google Scholar
• Wang , H. 2012 . Available at http://www.stat.colostate.edu/~wanghn/Tree.html
   Google Scholar
• Wang , H. and Marron , J. 2007 . “Object Oriented Data Analysis: Sets of Trees,” . The Annals of Statistics , 35 ( 5 ) : 1849 – 1873 .
   Web of Science ®Google Scholar