Multiplicative bias correction for inverse gamma and beta prime kernel density estimators

References

• Bouezmarni, T., and O. Scaillet. 2005. Consistency of asymmetric kernel density estimators and smoothed histograms with application to income data. Econometric Theory 21 (2):390–412. doi: 10.1017/S0266466605050218.
   Web of Science ®Google Scholar
• Chen, S. X. 1999. Beta kernel estimators for density functions. Computational Statistics & Data Analysis 31 (2):131–45. doi: 10.1016/S0167-9473(99)00010-9.
   Web of Science ®Google Scholar
• Chen, S. X. 2000. Gamma kernel estimators for density functions. Annals of the Institute of Statistical Mathematics 52 (3):471–80. doi: 10.1023/A:1004165218295.
   Web of Science ®Google Scholar
• Erçelik, E., and M. Nadar. 2020. Nonparametric density estimation based on beta prime kernel. Communications in Statistics - Theory and Methods 49 (2):325–42. doi: 10.1080/03610926.2018.1538458.
   Web of Science ®Google Scholar
• Funke, B., and R. Kawka. 2015. Nonparametric density estimation for multivariate bounded data using two non-negative multiplicative bias correction methods. Computational Statistics & Data Analysis 92:148–62. doi: 10.1016/j.csda.2015.07.006.
   Web of Science ®Google Scholar
• Gustafsson, J., M. Hagmann, J. P. Nielsen, and O. Scaillet. 2009. Local transformation kernel density estimation of loss distributions. Journal of Business & Economic Statistics 27 (2):161–75. doi: 10.1198/jbes.2009.0011.
   Web of Science ®Google Scholar
• Hagmann, M., and O. Scaillet. 2007. Local multiplicative bias correction for asymmetric kernel density estimators. Journal of Econometrics 141 (1):213–49. doi: 10.1016/j.jeconom.2007.01.018.
   Web of Science ®Google Scholar
• Harfouche, L., S. Adjabi, and N. Zougab. 2018a. Bayesian bandwidth selection with two multiplicative bias correction estimators for discrete kernel. Communication in statistics-Case studies. Data Analysis and Applications doi: 10.1080/23737484.2018.1512909.
   Google Scholar
• Harfouche, L., S. Adjabi, N. Zougab, and B. Funke. 2018b. Multiplicative bias correction for discrete kernels. Statistical Methods & Applications 27 (2):253–76. doi: 10.1007/s10260-017-0395-x.
   Web of Science ®Google Scholar
• Hirukawa, M. 2010. Nonparametric multiplicative bias correction for kernel-type density estimation on the unit interval. Computational Statistics & Data Analysis 54 (2):473–95. doi: 10.1016/j.csda.2009.09.017.
   Web of Science ®Google Scholar
• Hirukawa, M., and M. Sakudo. 2014. Nonnegative bias reduction methods for density estimation using asymmetric kernels. Computational Statistics & Data Analysis 75:112–23. doi: 10.1016/j.csda.2014.01.012.
   Web of Science ®Google Scholar
• Jin, X., and J. Kawczak. 2003. Birnbaum-Saunders and lognormal kernel estimators for modelling durations in high frequency financial data. Annals of Economics and Finance 4:103–24.
   Google Scholar
• Jones, M. C., O. Linton, and J. P. Nielsen. 1995. A simple bias reduction method for density estimation. Biometrika 82 (2):327–38. doi: 10.1093/biomet/82.2.327.
   Web of Science ®Google Scholar
• Leiva, V., F. Vilca, N. Balakrishnan, and A. Sanhueza. 2010. A skewed Sinh-Normal distribution and its properties and application to air pollution. Communications in Statistics - Theory and Methods 39 (3):426–43. doi: 10.1080/03610920903140171.
   Web of Science ®Google Scholar
• Marchant, C., K. Bertin, V. Leiva, and H. Saulo. 2013. Generalized Birnbaum-Saunders kernel density estimators and an analysis of financial data. Computational Statistics & Data Analysis 63:1–15. doi: 10.1016/j.csda.2013.01.013.
   Web of Science ®Google Scholar
• Mousa, A. M., M. K. Hassan, and A. Fathi. 2016. A new nonparametric estimator for pdf based on inverse gamma distribution. Communications in Statistics - Theory and Methods 45 (23):7002–10. doi: 10.1080/03610926.2014.972575.
   Web of Science ®Google Scholar
• Nadarajah, S. 2008. A truncated inverted beta distribution with application to air pollution data. Stochastic Environmental Research and Risk Assessment 22 (2):285–9. doi: 10.1007/s00477-007-0120-7.
   Web of Science ®Google Scholar
• Saulo, H., V. Leiva, F. A. Ziegelmann, and C. Marchant. 2013. A nonparametric method for estimating asymmetric densities based on skewed Birnbaum-Saunders distributions applied to environmental data. Stochastic Environmental Research and Risk Assessment 27 (6):1479–91. doi: 10.1007/s00477-012-0684-8.
   Web of Science ®Google Scholar
• Scaillet, O. 2004. Density estimation using inverse and reciprocal inverse Gaussian kernels. Journal of Nonparametric Statistics 16 (1–2):217–26. doi: 10.1080/10485250310001624819.
   Web of Science ®Google Scholar
• Terrell, G. R., and D. W. Scott. 1980. On improving convergence rates for nonnegative kernel density estimators. Annals of Statistics 8:1160–3.
   Web of Science ®Google Scholar
• Zougab, N., and S. Adjabi. 2016. Multiplicative bias correction for generalized Birnbaum-Saunders kernel density estimators and application to nonnegative heavy tailed data. Journal of the Korean Statistical Society 45 (1):51–63. doi: 10.1016/j.jkss.2015.07.001.
   Web of Science ®Google Scholar
• Zougab, N., L. Harfouche, Y. Ziane, and S. Adjabi. 2018. Multivariate generalized Birnbaum-Saunders kernel density estimators. Journal of Communication in Statistics Theory and Methods 47 (18):4534–4555.
   Web of Science ®Google Scholar