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Original Articles

Testing symmetry of a nonparametric bivariate regression function

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Pages 547-565 | Received 01 Dec 2009, Accepted 08 Nov 2010, Published online: 12 May 2011

References

  • Ahmad , I. A. and Li , Q. 1997 . Testing Symmetry of an Unknown Density Function by Kernel Method . Journal of Nonparametric Statistics , 7 : 279 – 293 .
  • Atallah , M. J. 1985 . On Symmetry Detection . IEEE Transactions on Computers , C-34 : 663 – 666 .
  • Berger , J. O. and Delampady , M. 1987 . Testing Precise Hypotheses, . Statistical Science , 2 : 317 – 352 .
  • Birke , M. 2008 . Central Limit Theorems for the Integrated Squared Error of Derivative Estimators . Statistics and Probability Letters , 78 : 1903 – 1913 .
  • Bissantz , N. , Holzmann , H. and Pawlak , M. 2009 . Testing for Image Symmetries – with Application to Confocal Microscopy . IEEE Transactions on Information Theory , 55 ( 4 ) : 1841 – 1855 .
  • Cabaña , A. and Cabaña , M. 2000 . Tests of Symmetry Based On Transformed Empirical Processes . Canadian Journal of Statistics , 28 : 829 – 839 .
  • Conway , J. H. , Burgiel , H. and Goodman-Strauss , C. 2008 . Symmetries of Things , Wellesley, MA : AK Peters .
  • Dette , H. and Neumeyer , N. 2001 . Nonparametric Analysis Of Covariance . Annals of Statistics , 29 : 1361 – 1400 .
  • Dette , H. , Kusi-Appiah , S. and Neumeyer , N. 2002 . Testing Symmetry in Nonparametric Regression Models . Journal of Nonparametric Statistics , 14 ( 5 ) : 477 – 494 .
  • Fan , Y. and Linton , O. 2003 . Some Higher Order Theory for a Consistent Nonparametric Model Specification Test . Journal of Statistical Planning and Inference , 109 : 125 – 154 .
  • Friedberg , S. A. 1986 . Finding Axes of a Skewed Symmetry . Computer Vision Graphics Image Processing , 32 : 138 – 155 .
  • Ghosh , B. K. and Huang , W.-M. 1991 . The Power and Optimal Kernel of the Bickel-Rosenblatt Test for Goodness of Fit . Annals of Statistics , 19 : 999 – 1009 .
  • Gijbels , I. , Lambert , A. and Qiu , P. 2007 . Jump-Preserving Regression and Smoothing Using Local Linear Fitting: A Compromise . Annals of Institute of Statistical Mathematics , 59 : 235 – 272 .
  • Giné , E. and Guillou , A. 2002 . Rates of Strong Uniform Consistency for Multivariate Kernel Density Estimators . Annales de l’ Institut Henri Poincaré , 6 : 907 – 921 .
  • Gratt , B. M. , Shetty , V. , Saiar , M. and Sickles , E. A. 1995 . Electronic Thermography for the Assessment of Inferior Alveolar Nerve Deficit . Oral Surgery, Oral Medicine, Oral Pathology, Oral Radiology Endodontics , 80 : 153 – 160 .
  • Hall , P. 1984 . Integrated Square Error Properties of Kernel Estimators of Regression Functions . Annals of Statistics , 12 ( 1 ) : 214 – 260 .
  • Hall , P. and Heyde , C. C. 1980 . Martingale Limit Theory and its Application , 52 – 53 . New York : Academic .
  • Hall , P. , Qiu , P. and Rau , C. 2008 . Tracking Edges, Corners and Vertices in an Image . Scandinavian Journal of Statistics , 35 : 1 – 17 .
  • Härdle , W. and Mammen , E. 1993 . Testing Parametric Versus Nonparametric Regression . Annals of Statistics , 21 : 1926 – 1947 .
  • Hollander , M. 1988 . “ Testing for Symmetry ” . In Encylopaedia in Statistical Sciences Edited by: Johnson , N. L. and Kotz , S. Vol. 9 , 211 – 216 .
  • Hušková , M. 1984 . Hypothesis of Symmetry . Handbook of Statistics, Nonparametric Methods , 4 North Holland, Amsterdam, pp. 63–78
  • Jones , B. F. 1998 . A Reappraisal of the Use of Infrared Thermal Image Analysis in Medicine . IEEE Transactions on Medical Imaging , 17 : 1019 – 1027 .
  • Kiryathi , N. and Gofman , Y. 1998 . Detecting Symmtery in Grey Level Images: The Global Optimization Approach . International Journal of Computer Vision , 29 : 29 – 45 .
  • Kuruganti , P. T. and Qi , H. Asymmetry Analysis in Breast Cancer Detection Using Thermal Infrared Images . Proc. of the 2nd Joint EMBS-BMES Conference . Houston. Vol. 2 , pp. 1129 – 1130 .
  • Loy , G. and Zelinsky , A. 2003 . Fast Radial Symmetry For Detecting Points of Interest . IEEE Transactions on Pattern Analysis and Machine Intelligence , 25 : 595 – 973 .
  • Mallows , C. L. 1972 . A Note on Asymptotic Joint Normality . Annals of Mathematical Statistics , 43 : 508 – 515 .
  • Marola , G. 1989 . On the Detection of the Axes of Symmtery of Symmetric and Almost Symmetric Planar Images . IEEE Transactions on Pattern Analysis and Machine Intelligence , 11 : 104 – 108 .
  • Rosen , J. 1995 . Symmetry in Science , New York : Springer-Verlag .
  • Rosenblatt , M. 1975 . A Quadratic Measure of Deviation of Two-Dimensional Density Estimates and a Test of Independence . Annals of Statistics , 3 : 1 – 14 .
  • Stahljans, K. (2007), ‘Symmetrietests in Multivariaten Nichtparametrischen Modellen’, Diploma thesis, Ruhr-Universität Bochum (in German)
  • Wand , M. P. and Jones , M. C. 1995 . Kernel Smoothing , London : Chapman and Hall .
  • Weyl , H. 1952 . Symmetry , Princeton : Princeton University Press .
  • Wu , C. F.J. 1986 . Jackknife, Bootstrap and Other Resampling Methods in Regression Analysis . Annals of Statistics , 14 : 1261 – 1295 .
  • Xiao , Z. , Hou , Z. , Miao , C. and Wang , J. 2005 . Using Phase Information for Symmetry Detection . Pattern Recognition Letters , 26 : 1985 – 1994 .

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