Density estimation via the random forest method

References

• Bose, A., and S. Dutta, 2013. Density estimation using bootstrap bandwidth selector. Statistics & Probability Letters 83:245–56.
   Web of Science ®Google Scholar
• Botev, Z. I., J. F. Grotowski, D. P. Kroese. 2010. Kernel densityestimation via diffusion. The Annals of Statistics 38(5):2916–57.
   Web of Science ®Google Scholar
• Breiman, L. 1996. Out-of-bag estimation. Technical report, Citeseer.
   Google Scholar
• Breiman, L., 2001. Random forests. Machine Learning 45(1):5–32.
   Web of Science ®Google Scholar
• Cao, R., A. Cuevas, and W. G. Manteiga, 1994. A comparative study of several smoothing methods in density estimation. Computational Statistics & Data Analysis 17:153–76.
   Web of Science ®Google Scholar
• Chan, N.-H., T. C. Lee, and L. Peng, 2010. On nonparametric local inference for density estimation. Computational Statistics & Data Analysis 54(2):509–15.
   Web of Science ®Google Scholar
• Dutta, S., 2014. Local smoothing using the bootstrap. Communications in Statistics-Simulation and Computation 43(2):378–89.
   Web of Science ®Google Scholar
• Dutta, S., 2015. Local smoothing for kernel distribution function estimation. Communications in Statistics-Simulation and Computation 4(4):878–91.
   Web of Science ®Google Scholar
• Eguchi, S., and J. Copas. 2006. Interpreting Kullback Leibler divergence with the neyman-pearson lemma. Journal of Multivariate Analysis 97 (9):2034–40. Special Issue dedicated to Prof. Fujikoshi.
   Web of Science ®Google Scholar
• Han, B., D. Comaniciu, Y. Zhu, and L. S. Davis, 2008. Sequential kernel density approximation and its application to real-time visual tracking. Pattern Analysis and Machine Intelligence, IEEE Transactions on 30(7):1186–97.
   PubMed Web of Science ®Google Scholar
• Hazelton, M. L., 1999. An optimal local bandwidth selector for kernel density estimation. Journal of Statistical Planning and Inference 77(1):37–50.
   Web of Science ®Google Scholar
• Izenman, A. J., 1991. Review papers: recent developments in nonparametric density estimation. Journal of the American Statistical Association 86(413):205–24.
   Web of Science ®Google Scholar
• Kleiber, C., and S. Kotz. 2003. Statistical size distributionsin economics and actuarial sciences, Volume 470. Hoboken, New Jersey: John Wiley & Sons.
   Google Scholar
• Klemelä, J. 2009. Smoothing of Multivariate Data: Density Estimation and Visualization, Volume 737. Hoboken, New Jersey: John Wiley & Sons.
   Google Scholar
• Lu, L., H. Jiang, and W. H. Wong, 2013. Multivariate density estimation by Bayesian Sequential Partitioning. Journal of the American Statistical Association 108(504):1402–10.
   Web of Science ®Google Scholar
• Lugosi, G., A. Nobel. 1996. Consistency of data-driven histogrammethods for density estimation and classification. The Annals of Statistics 24(2):687–706.
   Web of Science ®Google Scholar
• Miecznikowski, J. C., D. Wang, and A. Hutson, 2010. Bootstrap mise estimators to obtain bandwidth for kernel density estimation. Communications in Statistics-Simulation and Computation 39(7):1455–69.
   Web of Science ®Google Scholar
• Parzen, E., 1962. On estimation of a probability density function and mode. The Annals of Mathematical Statistics 33(3):1065–76.
   Google Scholar
• Rosenblatt, M. 1956. Remarks on some nonparametricestimates of a density function. The Annals of Mathematical Statistics 27(3):832–7.
   Google Scholar
• Seghouane, A.-K., and S.-I. Amari, 2007. The AIC criterion and symmetrizing the Kullback–Leibler divergence. Neural Networks, IEEE Transactions on 18(1):97–106.
   PubMed Web of Science ®Google Scholar
• Sheather, S. J., 1986. An improved data-based algorithm for choosing the window width when estimating the density at a point. Computational Statistics & Data Analysis 4(1):61–5.
   Web of Science ®Google Scholar
• Sheather, S. J. 2004. Density estimation. StatisticalScience 19(4):588–97.
   Google Scholar
• Sheather, S. J., and M. C. Jones, 1991. A reliable data-based bandwidth selection method for kernel density estimation. Journal of the Royal Statistical Society. Series B (Methodological) 53(3):683–90.
   Web of Science ®Google Scholar
• Silverman, B. W. 1986. Density estimation forstatistics and data analysis, Volume 26. Boca Raton, FL: CRC Press.
   Google Scholar
• Team, R. C. 2014. R: A language and environment for statistical computing. r foundation for statistical computing, vienna, austria. 2013.
   Google Scholar
• Wong, W. H., L. Ma. 2010. Optional pólya tree and Bayesian inference. The Annals of Statistics 38(3):1433–59.
   Web of Science ®Google Scholar
• Yang, K., and W. H. Wong. 2014. Density estimation via adaptive partition and discrepancy control. arXiv preprint arXiv:1404.1425.
   Google Scholar