Asymptotic properties of the normalised discrete associated-kernel estimator for probability mass function

References

• Abdous, B., and Kokonendji, C.C. (2009), ‘Consistency and Asymptotic Normality for Discrete Associated-Kernel Estimator’, African Diaspora Journal of Mathematics, 8, 63–70.
   Google Scholar
• Aitchison, J., and Aitken, C.G.G. (1976), ‘Multivariate Binary Discrimination by the Kernel Method’, Biometrika, 63, 413–420.
   Web of Science ®Google Scholar
• Chu, C.-Y., Henderson, D.J., and Parmeter, C.F. (2017), ‘On Discrete Epanechnikov Kernel Functions’, Computational Statistics and Data Analysis, 116, 79–105.
   Web of Science ®Google Scholar
• Devroye, L., and Lugosi, G. (2001), Combinatorial Methods in Density Estimation, New York: Springer.
   Google Scholar
• Glad, I.K., Hjort, N.L., and Ushakov, N.G. (2003), ‘Correction of Density Estimators That are Not Densities’, Scandinavian Journal of Statistics, 30, 415–427.
   Web of Science ®Google Scholar
• Fung, T., Alwan, A., Wishart, J., and Huang, A. (2020), mpcmp: Mean Parametrized Conway-Maxwell Poisson Regression (Ver. 0.3.6), R package. Available at http://cran.r-project.org/.
   Google Scholar
• Gaunt, R.E., Iyengar, S., Olde Daalhuis, A.B., and Simsek, B. (2019), ‘An Asymptotic Expansion for the Normalizing Constant of the Conway-Maxwell-Poisson Distribution’, Annals of the Institute of Statistical Mathematics, 71, 163–180.
   Web of Science ®Google Scholar
• Harfouche, L., Adjabi, S., Zougab, N., and Funke, B. (2018), ‘Multiplicative Bias Correction for Discrete Kernels’, Statistical Methods and Applications, 27, 253–276.
   Web of Science ®Google Scholar
• Hoeffding, W. (1963), ‘Probability Inequalities for Sums of Bounded Random Variables’, Journal of the American Statistical Association, 58, 13–30.
   Web of Science ®Google Scholar
• Huang, A. (2017), ‘Mean-Parametrized Conway-Maxwell-Poisson Regression Models for Dispersed Counts’, Statistical Modelling, 17, 359–380.
   Web of Science ®Google Scholar
• Huang, A., Sippel, L., and Fung, T. (2022), ‘Consistent Second-Order Discrete Kernel Smoothing Using Dispersed Conway-Maxwell-Poisson Kernels’, Computational Statistics, 37, 551–563.
   Web of Science ®Google Scholar
• Kokonendji, C.C., Mizère, D., and Balakrishnan, N. (2008), ‘Connections of the Poisson Weight Function to Overdispersion and Underdispersion’, Journal of Statistical Planning and Inference, 138, 1287–1296.
   Web of Science ®Google Scholar
• Kokonendji, C.C., and Senga Kiessé, T. (2011), ‘Discrete Associated Kernels Method and Extensions’, Statistical Methodology, 8, 497–516.
   Web of Science ®Google Scholar
• Kokonendji, C.C., Senga Kiessé, T., and Zocchi, S.S. (2007), ‘Discrete Triangular Distributions and Non-Parametric Estimation for Probability Mass Function’, Journal of Nonparametric Statistics, 19, 241–254.
   Web of Science ®Google Scholar
• Kokonendji, C.C., and Somé, S.M. (2018), ‘On Multivariate Associated Kernels to Estimate General Density Functions’, Journal of the Korean Statistical Society, 47, 112–126.
   Web of Science ®Google Scholar
• Kokonendji, C.C., and Somé, S.M. (2021), ‘Bayesian Bandwidths in Semiparametric Modelling for Nonnegative Orthant Data With Diagnostics’, Stats, 4, 162–183.
   Google Scholar
• Kokonendji, C.C., and Varron, D. (2016), ‘Performance of the Discrete Associated Kernel Estimator Through the Total Variation Distance’, Statistics and Probability Letters, 110, 225–235.
   Web of Science ®Google Scholar
• Kokonendji, C.C., and Zocchi, S.S. (2010), ‘Extensions of Discrete Triangular Distributions and Boundary Bias in Kernel Estimation for Discrete Functions’, Statistics and Probability Letters, 80, 1655–1662.
   Web of Science ®Google Scholar
• Li, Q., and Racine, J. (2003), ‘Nonparametric Estimation of Distributions With Categorical and Continuous Data’, Journal of Multivariate Analysis, 86, 266–292.
   Web of Science ®Google Scholar
• Ouyang, D., Li, Q., and Racine, J. (2006), ‘Cross-Validation and the Estimation of Probability Distributions With Categorical Data’, Journal of Nonparametric Statistics, 18, 69–100.
   Web of Science ®Google Scholar
• R Core Team (2021), R: A language and environment for statistical computing, Vienna, Austria: R Foundation for Statistical Computing. Available at http://cran.r-project.org/.
   Google Scholar
• Racine, J., Li, Q., and Yan, K.X. (2020), ‘Kernel Smoothed Probability Mass Functions for Ordered Datatypes’, Journal of Nonparametric Statistics, 32, 563–586.
   Web of Science ®Google Scholar
• Senga Kiessé, T. (2017), ‘On Finite Sample Properties of Nonparametric Discrete Asymmetric Kernel Estimators’, Statistics, 51, 1046–1060.
   Web of Science ®Google Scholar
• Senga Kiessé, T., and Cuny, H.E. (2014), ‘Discrete Triangular Associated Kernel and Bandwidth Choices in Semiparametric Estimation for Count Data’, Journal of Statistical Computation and Simulation, 84, 1813–1829.
   Web of Science ®Google Scholar
• Senga Kiessé, T., and Ventura, A. (2016), ‘Discrete Non-Parametric Kernel Estimation for Global Sensitivity Analysis’, Reliability Engineering and System Safety, 146, 47–54.
   Web of Science ®Google Scholar
• Shmueli, G., Minka, T.P., Kadane, J.B., Borle, S., and Boatwright, P. (2005), ‘A Useful Distribution for Fitting Discrete Data: Revival of the Conway-Maxwell-Poisson Distribution’, Journal of the Royal Statistical Society, Series C, 54, 127–142.
   Web of Science ®Google Scholar
• Toledo, D., Umetsu, C.A., Camargo, A.F.M., and Rodrigues de Lara, I.A. (2022), ‘Flexible Models for Non-Equidispersed Count Data: Comparative Performance of Parametric Models to Deal With Underdispersion’, AStA Advances in Statistical Analysis, 106, 473–497.
   Web of Science ®Google Scholar
• Wang, M., and Van Ryzin, J. (1981), ‘A Class of Smooth Estimators for Discrete Distributions’, Biometrika, 68, 301–309.
   Web of Science ®Google Scholar
• Wansouwé, W.E., Somé, S.M., and Kokonendji, C.C. (2016), ‘Ake: An R Package for Discrete and Continuous Associated Kernel Estimations’, The R Journal, 8, 258–276.
   Google Scholar