Multivariate Density Estimation by Bayesian Sequential Partitioning

REFERENCES

• Barron , A. R. , Gyorfi , L. and van der Meulen , E. C. 1992 . Distribution Estimation Consistent in Total Variation and in Two Types of Information Divergence . IEEE Transactions on Information Theory , 38 : 1437 – 1454 .
   Web of Science ®Google Scholar
• Fan , J. and Marron , J. 1994 . Fast Implementations of Nonparametric Curve Estimators . Journal of Computational and Graphical Statistics , 3 : 35 – 56 .
   Google Scholar
• Bache , K. and Lichman , M . 2013 . UCI Machine Learning Repository , available at http://archive.ics.uci.edu/ml.
   Google Scholar
• Frey , P. W. and Slate , D. J. 1991 . Letter Recognition Using Holland-Style Adaptive Classifiers . Machine Learning , 6 : 161 – 182 .
   Web of Science ®Google Scholar
• Gordon , N. , Salmond , D. J. and Smith , A. F. M. 1993 . “ Novel Approach to Nonlinear/Non-Gaussian Bayesian State Estimation ” . In IEE Proceedings on Radar and Signal Processing Vol. 140 , 107 – 113 .
   Google Scholar
• Gray , A. G. 2003 . Nonparametric Density Estimation: Toward Computational Tractability . SIAM International Conference on Data Mining , : 203 – 211 .
   Google Scholar
• Gray , R. M. and Olshen , R. A. 1997 . “ Vector Quantization and Density Estimation ” . In Proceedings of the Compression and Complexity of Sequences, 11–13 June 1997 172 – 193 .
   Google Scholar
• Heck , D. , Knapp , J. , Capdevielle , J. , Schatz , G. and Thouw , T. 1998 . Corsika: A Monte Carlo Code to Simulate Extensive Air Showers . Forschungszentrum Karlsruhe FZKA , : 6019
   Google Scholar
• Ihler , A. 2003 . Kernel Density Estimation Toolbox, available at http://www.ics.uci.edu/ihler/code/kde.html
   Google Scholar
• Jones , M. C. , Marron , J. S. and Sheather , S. J. 1996 . A Brief Survey of Bandwidth Selection for Density Estimation . Journal of the American Statistical Association , 91 : 401 – 407 .
   Web of Science ®Google Scholar
• Klemela , J. 2009 . Smoothing of Multivariate Data Density Estimation and Visualization , New York : Wiley .
   Google Scholar
• Kong , A. , Liu , J. S. and Wong , W. H. 1994 . Sequential Imputations and Bayesian Missing Data Problems . Journal of the American Statistical Association , 89 : 278 – 288 .
   Web of Science ®Google Scholar
• Liu , J. S. 2001 . Monte Carlo Strategies in Scientific Computing (Springer Series in Statistics) , New York : Springer .
   Google Scholar
• Liu , J. S. , Chen , R. and Wong , W. H. 1998 . Rejection Control and Sequential Importance Sampling . Journal of the American Statistical Association , 93 : 1022 – 1031 .
   Web of Science ®Google Scholar
• Lugosi , G. and Nobel , A. 1996 . Consistency of Data-Driven Histogram Methods for Density Estimation and Classification . The Annals of Statistics , 24 : 687 – 706 .
   Web of Science ®Google Scholar
• Parzen , E. 1962 . On Estimation of a Probability Density Function and Mode . The Annals of Mathematical Statistics , 33 : 1065 – 1076 .
   Google Scholar
• Pavlov , D. , Popescul , A. , Pennock , D. M. and Ungar , L. H. 2002 . Mixtures of Conditional Maximum Entropy Models . Proceedings of the ICML-2003 , : 584 – 591 .
   Google Scholar
• Pavlov , D. , Popescul , A. , Pennock , D. M. and Ungar , L. H. 2011 . R: A Language and Environment for Statistical Computing R Development Core Team, , Vienna, Austria : R Foundation for Statistical Computing .
   Google Scholar
• Rosenblatt , M. 1956 . Remarks on Some Nonparametric Estimates of a Density Function . Annals of Mathematical Statistics , 27 : 832 – 837 .
   Google Scholar
• Scott , D. W. 1979 . On Optimal and Data-Based Histograms . Biometrika , 66 : 605 – 610 .
   Web of Science ®Google Scholar
• Scott , D. W. 1985 . Averaged Shifted Histograms: Effective Nonparametric Density Estimators in Several Dimensions . The Annals of Statistics , 13 : 1024 – 1040 .
   Web of Science ®Google Scholar
• Silverman , B. W. 1986 . Density Estimation for Statistics and Data Analysis , Boca Raton, FL : Chapman & Hall/CRC .
   Google Scholar
• Simonoff , J. S. 1996 . Smoothing Methods in Statistics (Springer Series in Statistics), , New York : Springer .
   Google Scholar
• Terrell , G. R. 1990 . The Maximal Smoothing Principle in Density Estimation . Journal of the American Statistical Association , 85 : 470 – 477 .
   Web of Science ®Google Scholar
• Wand , M. P. 1994 . Fast Computation of Multivariate Kernel Estimators . Journal of Computational and Graphical Statistics , 3 : 433 – 445 .
   Google Scholar
• Wong , W. H. and Ma , L. 2010 . Optional Polya Tree and Bayesian Inference . The Annals of Statistics , 38 : 1433 – 1459 .
   Web of Science ®Google Scholar
• Yang , C. , Duraiswami , R. , Gumerov , N. A. and Davis , L. 2003 . “ Improved Fast Gauss Transform and Efficient Kernel Density Estimation ” . In Computer Vision, 2003. Proceedings. Ninth IEEE International Conference on Vol. 1 , 664 – 671 .
   Google Scholar