Two new nonparametric kernel distribution estimators based on a transformation of the data

References

• I.S. Abramson, On bandwidth variation in kernel estimates – a square root law, Ann. Stat. 10 (1982), pp. 1217–1223. doi: 10.1214/aos/1176345986
   Web of Science ®Google Scholar
• R. Bojanic and E. Seneta, A unified theory of regularly varying sequences, Math. Z. 134 (1973), pp. 91–106. doi: 10.1007/BF01214468
   Web of Science ®Google Scholar
• J. Galambos and E. Seneta, Regularly varying sequences, Proc. Amer. Math. Soc. 41 (1973), pp. 110–116. doi: 10.1090/S0002-9939-1973-0323963-5
   Web of Science ®Google Scholar
• P. Janssen, J. Swanepoel, and N. Veraverbeke, Modifying the kernel distribution function estimator towards reduced bias, Statistics 41 (2007), pp. 93–103. doi: 10.1080/02331880601106561
   Web of Science ®Google Scholar
• M.C. Jones, O. Linton, and J.P. Nielsen, A simple bias reduction method for density estimation, Biometrika 82 (1995), pp. 327–338. doi: 10.1093/biomet/82.2.327
   Web of Science ®Google Scholar
• J.S. Marron and M.P. Wand, Exact mean integrated squared error, Ann. Stat. 20 (1992), pp. 712–736. doi: 10.1214/aos/1176348653
   Web of Science ®Google Scholar
• J. Milet, G. Nuel, L. Watier, D. Courtin, Y. Slaoui, P. Senghor, F. Migot-Nabias, O. Gaye, and A. Garcia, Genome wide linkage study, using a 250K SNP map, of Plasmodium falciparum infection and mild malaria attack in a Senegalese population, PLoS One 5 (2010), pp. e11616. doi: 10.1371/journal.pone.0011616
   PubMed Web of Science ®Google Scholar
• A. Mokkadem and M. Pelletier, A companion for the Kiefer-Wolfowitz-Blum stochastic approximation algorithm, Ann. Stat. 35 (2007), pp. 1749–1772. doi: 10.1214/009053606000001451
   Web of Science ®Google Scholar
• A. Mokkadem, M. Pelletier, and Y Slaoui, The stochastic approximation method for the estimation of a multivariate probability density, J. Stat. Plan. Inference 139 (2009), pp. 2459–2478. doi: 10.1016/j.jspi.2008.11.012
   Web of Science ®Google Scholar
• E.A. Nadaraya, Some new estimates for distribution functions, Theory Prob. Appl. 9 (1964), pp. 497–500. doi: 10.1137/1109069
   Google Scholar
• D. Ruppert and D.B. Cline, Bias reduction in kernel density estimation by smoothed empirical transformations, Ann. Stat. 22 (1994), pp. 185–210. doi: 10.1214/aos/1176325365
   Web of Science ®Google Scholar
• M. Samiuddin and G.M. El-Sayyad, On nonparametric kernel density estimates, Biometrika 77 (1990), pp. 865–874. doi: 10.1093/biomet/77.4.865
   Web of Science ®Google Scholar
• B.W. Silverman, Density Estimation for Statistics and Data Analysis, Chapman and Hall, London, 1986.
   Google Scholar
• Y. Slaoui, Bandwidth selection for recursive kernel density estimators defined by stochastic approximation method, J. Probab. Stat. 2014 (2014a), ID 739640, doi:10.1155/2014/739640
   Google Scholar
• Y. Slaoui, The stochastic approximation method for the estimation of a distribution function, Math. Methods Stat. 23 (2014b), pp. 306–325. doi: 10.3103/S1066530714040048
   Google Scholar
• Y. Slaoui, Bias reduction in kernel density estimation, J. Nonparametr. Stat. 30 (2018), pp. 505–522. doi: 10.1080/10485252.2018.1442927
   Web of Science ®Google Scholar
• Y. Slaoui, Automatic bandwidth selection for recursive kernel density estimators with length-biased data, Jpn. J. Stat. Data Sci. 0 (2019), doi: 10.1007/s42081-019-00053-z
   Google Scholar
• Y. Slaoui and G. Nuel, Parameter estimation in a hierarchical random intercept model with censored response approach using a SEM algorithm and Gibbs sampling, Sankhya B 76 (2014c), pp. 210–233. doi: 10.1007/s13571-014-0081-z
   Google Scholar
• J.W.H. Swanepoel, Mean intergrated squared error properties and optimal kernels when estimating a distribution function, Comm. Stat. Theory Methods 17 (1988), pp. 3785–3799. doi: 10.1080/03610928808829835
   Web of Science ®Google Scholar
• J.W.H. Swanepoel and F.C. Van Graan, A new kernel distribution function estimator based on a nonparametric transformation of the data, Scand. J. Stat. 32 (2005), pp. 551–562. doi: 10.1111/j.1467-9469.2005.00472.x
   Web of Science ®Google Scholar
• C. Tenreiro, Asymptotic behaviour of multistage plug-in bandwidth selections for kernel distribution function estimators, J. Nonparametr. Stat. 18 (2006), pp. 101–116. doi: 10.1080/10485250600578334
   Web of Science ®Google Scholar