References
- Abramson, I. S. 1982. On bandwidth variation in kernel estimates-a square root law. The Annals of Statistics 10 (4):1217–23. doi:10.1214/aos/1176345986.
- Breiman, L., W. Meisel, and E. Purcell. 1977. Variable kernel estimates of multivariate densities. Technometrics 19 (2):135–44. doi:10.1080/00401706.1977.10489521.
- Chacón, J. E. 2009. Data-driven choice of the smoothing parametrization for kernel density estimators. Canadian Journal of Statistics 37 (2):249–65. doi:10.1002/cjs.10016.
- Chacón, J. E., and T. Duong. 2010. Multivariate plug-in bandwidth selection withunconstrained pilot bandwidth matrices. TEST 19 (2):375–98. doi:10.1007/s11749-009-0168-4.
- Duong, T., and M. Hazelton. 2003. Plug-in bandwidth matrices for bivariate kernel density estimation. Journal of Nonparametric Statistics 15 (1):17–30. doi:10.1080/10485250306039.
- Givens, G. H., and J. A. Hoeting. 2013. Computational statistics. 2nd ed. Hoboken, NJ: John Wiley & Sons, Inc.
- Jones, M. C., J. S. Marron, and S. J. Sheather. 1996. A brief survey of bandwidth selection for density estimation. Journal of the American Statistical Association 91 (433):401–407. doi:10.1080/01621459.1996.10476701.
- Li, D., K. Yang, and W. H. Wong. 2016. Density estimation via discrepancy based adaptive sequential partition. Advances in Neural Information Processing Systems 29:1091–9.
- Loftsgaarden, D. O., and C. P. Quesenberry. 1965. A nonparametric estimate of a multivariate density function. The Annals of Mathematical Statistics 36 (3):1049–51. doi:10.1214/aoms/1177700079.
- Ozakin, A., and A. G. Gray. 2009. Submanifold density estimation. Advances in Neural Information Processing Systems 22:1375–82. Curran Associates, Inc.
- Parzen, E. 1962. On estimation of a probability density function and mode. The Annals of Mathematical Statistics 33 (3):1065–76. doi:10.1214/aoms/1177704472.
- Pelletier, B. 2005. Kernel density estimation on riemannian manifolds. Statistics & Probability Letters 73 (3):297–304. doi:10.1016/j.spl.2005.04.004.
- Rosenblatt, M. 1956. Remarks on some nonparametric estimates of a density function. The Annals of Mathematical Statistics 27 (3):832–37. doi:10.1214/aoms/1177728190.
- Sain, S. R. 2002. Multivariate locally adaptive density estimation. Computational Statistics & Data Analysis 39 (2):165–86. doi:10.1016/S0167-9473(01)00053-6.
- Saputro, D. R. S., and P. Widyaningsih. 2017. Limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method for the parameter estimation on geographically weighted ordinal logistic regression model (GWOLR). AIP Conference Proceedings 1868 (1):040009.
- Terrell, G. R. 1990. The maximal smoothing principle in density estimation. Journal of the American Statistical Association 85 (410):470–77. doi:10.1080/01621459.1990.10476223.
- Vapnik, V. 1982. Estimation of dependences based on empirical data. 1st ed. Berlin, Heidelberg: Springer-Verlag.
- Vincent, P., and Y. Bengio. 2003. Manifold parzen windows. Advances in Neural Information Processing Systems 15:849–56.
- Wand, M. P., and M. C. Jones. 1993. Comparison of smoothing parameterizations in bivariate kernel density estimation. Journal of the American Statistical Association 88 (422):520–28. doi:10.1080/01621459.1993.10476303.
- Wand, M. P., and M. C. Jones. 1995. Kernel smoothing. 1st ed. London: Chapman and Hall, Ltd.
- Wasserman, L. 2018. Topological data analysis. Annual Review of Statistics and Its Application 5 (1):501–32. doi:10.1146/annurev-statistics-031017-100045.
- Wu, T. J., C. F. Chen, and H. Y. Chen. 2007. A variable bandwidth selector in multivariate kernel density estimation. Statistics & Probability Letters 77 (4):462–67. doi:10.1016/j.spl.2006.08.013.