The Mode Tree: A Tool for Visualization of Nonparametric Density Features

References

• Abramson , I. S. 1982 . “On Bandwidth Variation in Kernel Estimates–a Square Root Law” . The Annals of Statistics , 10 : 1217 – 1223 .
   Web of Science ®Google Scholar
• Ahrens , L. H. 1965 . “Observations on the Fe-Si-Mg Relationship in Chondrites” . Geochimica et Cosmochimica Acta , 29 : 801 – 806 .
   Web of Science ®Google Scholar
• Babaud , J. , Witkin , A. P. , Baudin , M. and Duda , R. O. 1986 . “Uniqueness of the Gaussian Kernel for Scale-Space Filtering” . IEEE Transactions on Pattern Analysis and Machine Intelligence , PAMI-8 : 26 – 33 .
   Web of Science ®Google Scholar
• Breiman , L. , Meisel , W. and Purcell , E. 1977 . “Variable Kernel Estimates of Multivariate Densities” . Technometrics , 19 : 135 – 144 .
   Web of Science ®Google Scholar
• Eddy , W. F. 1980 . “Optimal Kernel Estimates of the Mode” . The Annals of Statistics , 8 : 870 – 882 .
   Web of Science ®Google Scholar
• Good , I. J. and Gaskins , R. A. 1980 . “Density Estimation and Bump-Hunting by the Penalized Maximum Likelihood Method Exemplified by Scattering and Meteorite Data” . Journal of the American Statistical Association , 75 : 42 – 73 .
   Web of Science ®Google Scholar
• Izenman , A. J. and Sommer , C. J. 1988 . “Philatelic Mixtures and Multimodal Densities” . Journal of the American Statistical Association , 83 : 941 – 953 .
   Web of Science ®Google Scholar
• Jones , M. C. 1990 . “Variable Kernel Density Estimates” . Australian Journal of Statistics , 32 : 361 – 371 .
   Google Scholar
• Mammen , E. 1991 . “Nonparametric Regression Under Qualitative Smoothness Assumptions” . The Annals of Statistics , 10 : 1217 – 1223 .
   Google Scholar
• Mammen , E. , Marron , J. S. and Fisher , N. I. 1992 . “Some Asymptotics for Multimodality Tests Based on Kernel Density Estimates” . Probability Theory and Related Fields , 91 : 115 – 132 .
   Web of Science ®Google Scholar
• Matthews , M. V. 1983 . “On Silverman's Test for the Number of Modes in a Univariate Density Function” , Harvard University, Dept. of Statistics . unpublished B.A. honors thesis
   Google Scholar
• Minnotte , M. C. 1992 . “A Test of Mode Existence With Applications to Multimodality” , Rice University, Dept. of Statistics . unpublished Ph.D. thesis
   Google Scholar
• Müller , D. W. and Sawitzki , G. 1991 . “Excess Mass Estimates and Tests for Multimodality” . Journal of the American Statistical Association , 86 : 738 – 746 .
   Web of Science ®Google Scholar
• Parzen , E. 1962 . “On Estimation of Probability Density Function and Mode” . The Annals of Mathematical Statistics , 33 : 1065 – 1076 .
   Google Scholar
• Roeder , K. 1990 . “Density Estimation With Confidence Sets Exemplified by Superclusters and Voids in the Galaxies” . Journal of the American Statistical Association , 85 : 617 – 624 .
   Web of Science ®Google Scholar
• Rosenblatt , M. 1956 . “Remarks on Some Nonparametric Estimates of a Density Function” . The Annals of Mathematical Statistics , 27 : 832 – 837 .
   Google Scholar
• Scott , D. W. 1992 . Multivariate Density Estimation: Theory, Practice, and Visualization , New York : John Wiley .
   Google Scholar
• Scott , D. W. , Gotto , A. M. , Cole , J. S. and Gorry , G. A. 1978 . “Plasma Lipids as Collateral Risk Factors in Coronary Heart Disease–A Study of 371 Males With Chest Pain” . Journal of Chronic Diseases , 31 : 337 – 345 .
   PubMedGoogle Scholar
• Silverman , B. W. 1981 . “Using Kernel Density Estimates to Investigate Multimodality” . Journal of the Royal Statistical Society , 43 : 97 – 99 . Ser. B
   Google Scholar
• Terrell , G. R. and Scott , D. W. 1985 . “Oversmoothed Nonparametric Density Estimates” . Journal of the American Statistical Association , 80 : 209 – 214 .
   Web of Science ®Google Scholar
• Terrell , G. R. and Scott , D. W. 1992 . “Variable Kernel Density Estimation” . The Annals of Statistics , 20 : 1236 – 1265 .
   Web of Science ®Google Scholar
• Tierney , L. 1990 . LISP-STAT: An Object-Oriented Environment for Statistical Computing and Dynamic Graphics , New York : John Wiley .
   Google Scholar
• Wand , M. P. , Marron , J. S. and Ruppert , D. 1991 . “Transformations in Density Estimation” . Journal of the American Statistical Association , 86 : 343 – 361 .
   Web of Science ®Google Scholar
• Wilson , I. G. 1983 . “Add a New Dimension to Your Philately” . The American Philatelist , 97 : 342 – 349 .
   Google Scholar