References
- Basu, A., Harris, I. R., Hjort, N. L., & Jones, M. C. (1998). Robust and efficient estimation by minimising a density power divergence. Biometrika, 85(3), 549–559. https://doi.org/https://doi.org/10.1093/biomet/85.3.549
- Bowman, A. W. (1984). An alternative method of cross-validation for the smoothing of density estimates. Biometrika, 71(2), 353–360. https://doi.org/https://doi.org/10.1093/biomet/71.2.353
- Cao, R., Cuevas, A., & Gonalez-Manteiga, W. (1994). A comparative study of several smoothing methods in density estimation? Computational Statistics and Data Analysis, 17(2), 153–176. https://doi.org/https://doi.org/10.1016/0167-9473(92)00066-Z
- Cichocki, A., Zdunek, R., & Amari, S. (2006). Csiszar's divergences for nonnegative matrix factorization: Family of new algorithms. In Lecture notes in computer science (pp. 32–39). Springer.
- Dhaker, H., Ngom, P., Deme, E., & Mbodj, M. (2018). New approach for bandwidth selection in the kernel density estimation based on β-divergence. Journal of Mathematical Sciences: Advances and Applications, 51(1), 57–83. https://doi.org/10.18642/jmsaa_7100121962
- Eguchi, S., & Kano, Y. (2001). Robustifying maximum likelihood estimation (Technical Report). Institute of Statistical Mathematics, June.
- Eugene, F. S. (1969). Estimation of a probability density function and its derivatives. The Annals of Mathematical Statistics, 40(4), 1187–1195. https://doi.org/https://doi.org/10.1214/aoms/1177697495
- Härdle, W. K. (1991). Smoothing techniques: With implementation in S. Springer Science and Business Media.
- Jones, M. C., Marron, J. S., & Sheather, S. J. (1996). A brief survey of bandwidth selection for density estimation. Journal of the American Statistical Association, 91(433), 401–407. https://doi.org/https://doi.org/10.1080/01621459.1996.10476701
- Jorgensen, B. (1997). The Theory of Dispersion Models. Chapman Hall/CRC Monographs on Statistics and Applied Probability.
- Kanazawa, Y. (1993). Hellinger distance and Kullback-Leibler loss for the kernel density estimator. Statistics and Probability Letters, 18(4), 315–321. https://doi.org/https://doi.org/10.1016/0167-7152(93)90022-B
- Mammen, E., Martinez-Miranda, M. D., Nielsen, J. P., & Sperlich, S. (2011). Do-validation for kernel density estimatio? Journal of the American Statistical Association, 106(494), 651–660. https://doi.org/https://doi.org/10.1198/jasa.2011.tm08687
- Mammen, E., Martinez-Miranda, M. D., Nielsen, J. P., & Sperlich, S. (2014). Further theoretical and practical insight to the do-validated bandwidth selector. Journal of the Korean Statistical Society, 43(3), 355–365. https://doi.org/https://doi.org/10.1016/j.jkss.2013.11.001
- Millimet, D. L., List, J. A., & Stengos, T. (2003). The Environmental Kuznets Curve: Real Progress or Misspecified Models. Review of Economics and Statistics, 85(4), 1038–1047. https://doi.org/https://doi.org/10.1162/003465303772815916
- Millimet, D. L., & Stengos, T. (2000). A semiparametric approach to modelling the environmental kuznets curve across U.S. States Department of Economics working paper, Southern Methodist University.
- Minami, M., & Eguchi, S. (2002). Robust blind source separation by Beta-divergence. Neural Comput., 14(8), 1859–1886. https://doi.org/https://doi.org/10.1162/089976602760128045
- Mugdadi, A. R., & Ibrahim, A. A. (2004). A bandwidth selection for kernel density estimation of functions of random variables. Computational Statistics and Data Analysis, 47(1), 49–62. https://doi.org/https://doi.org/10.1016/j.csda.2003.10.013
- Parzen, E. (1962). On estimation of a probability density function and mode. Annals of Mathematical Statistics, 33(3), 1065–1076. https://doi.org/https://doi.org/10.1214/aoms/1177704472
- Rudemo, M. (1982). Empirical choice of histograms and kernel density estimators. Scandinavia Journal of Statistics, 9(2), 65–78.
- Schmalensee, R., Stoker, T. M., & Judson, R. A. (1998). World Carbon Dioxide Emissions, 1950–2050. The Review of Economics and Statistics, 80(1), 15–27. https://doi.org/https://doi.org/10.1162/003465398557294
- Scott, W. D. (1992). Multivariate density estimation theory, practice, and visualization. Wiley.
- Silverman, B. W. (1986). Density estimation for statistics and data analysis. Chapman and Hall.
- Sultan, K. S., & Al-Moisheer, A. S. (2015). Mixture of inverse Weibull and lognormal distributions: Properties, estimation, and illustration. Mathematical Problems in Engineering, 2015. https://doi.org/https://doi.org/10.1155/2015/526786
- Taskin, F., & Zaim, O. (2000). Searching for a Kuznets Curve in Environmental Efficiency Using Kernel Estimation. Economics Letters, 68(2), 217–223. https://doi.org/https://doi.org/10.1016/S0165-1765(00)00250-0
- Turlach, B. A. (1993). Bandwidth selection in kernel density estimation: A review (Technical Report). Universite catholique de Louvain.
- Von Alven, W. H. (Ed.). (1964). Reliability engineering. Prentice Hall.
- Wand, M. P., & Jones, M. C. (1995). Kernel smoothing. Chapman and Hall.
- Xie, X., & Wu, J. (2014). Some Improvement on Convergence Rates of Kernel Density Estimator. Applied Mathematics, 5(11), 1684–1696. https://doi.org/https://doi.org/10.4236/am.2014.511161