B. Abdous and C. C. Kokonendji, Consistency and asymptotic normality for discrete associated-kernel estimator, African Diaspora Journal of Mathematics, vol.8, pp.63-70, 2009.

R. P. Agarwal and . M. Bohner, Basic Calculus on Time Scales and some of its Applications, Results in Mathematics, vol.44, issue.3, pp.3-22, 1999.
DOI : 10.1007/BF01444165

J. Aitchison and C. G. Aitken, Multivariate binary discrimination by the kernel method, Biometrika, vol.63, issue.3, pp.413-420, 1976.
DOI : 10.1093/biomet/63.3.413

A. Amiri, C. Crambes, and B. Thiam, Recursive estimation of nonparametric regression with functional covariate, Computational Statistics & Data Analysis, vol.69, pp.154-172, 2014.
DOI : 10.1016/j.csda.2013.07.030

URL : https://hal.archives-ouvertes.fr/hal-00750894

A. Antoniadis, Wavelets in statistics : a review (with discussion), Journal of the Italian Statistical Society Series B, vol.103, pp.97-144, 1997.
DOI : 10.1007/978-1-4612-2544-7

A. Azzalini and A. Bowman, A Look at Some Data on the Old Faithful Geyser, Applied Statistics, vol.39, issue.3, pp.357-365, 1990.
DOI : 10.2307/2347385

K. Bertin and N. Klutchnikoff, Adaptive estimation of a density function using beta kernels, ESAIM: Probability and Statistics, vol.18, pp.400-417, 2014.
DOI : 10.1007/978-1-4899-3324-9

M. Bohner and A. Peterson, Dynamic Equations on Time Scales, 2001.
DOI : 10.1007/978-1-4612-0201-1

M. Bohner and A. Peterson, Advances in Dynamic Equations on Time Scales, 2003.
DOI : 10.1007/978-0-8176-8230-9

S. Boucheron, G. Lugosi, and P. Massart, Concentration Inequalities : A Nonasymptotic Theory of Independence, 2013.
DOI : 10.1093/acprof:oso/9780199535255.001.0001

URL : https://hal.archives-ouvertes.fr/hal-00794821

T. Bouezmarni and J. V. Rombouts, Nonparametric density estimation for multivariate bounded data, Journal of Statistical Planning and Inference, vol.140, issue.1, pp.139-152, 2010.
DOI : 10.1016/j.jspi.2009.07.013

M. J. Brewer, A Bayesian model for local smoothing in kernel density estimation, Statistics and Computing, vol.10, issue.4, pp.299-309, 2000.
DOI : 10.1023/A:1008925425102

B. M. Brown and S. X. Chen, Beta-Bernstein Smoothing for Regression Curves with Compact Support, Scandinavian Journal of Statistics, vol.26, issue.1, pp.47-59, 1998.
DOI : 10.1111/1467-9469.00136

H. Cardot, A. De-moliner, and C. Goga, Estimating with kernel smoothers the mean of functional data in a finite population setting. A note on variance estimation in presence of partially observed trajectories, Statistics and Probability Letters 99, pp.156-166, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01075901

J. E. Chacón and T. Duong, Multivariate plug-in bandwidth selection with??unconstrained pilot bandwidth matrices, TEST, vol.9, issue.238, pp.375-398, 2010.
DOI : 10.1007/978-1-4899-4493-1

J. E. Chacón and T. Duong, UNCONSTRAINED PILOT SELECTORS FOR SMOOTHED CROSS-VALIDATION, Australian & New Zealand Journal of Statistics, vol.9, issue.238, pp.331-351, 2011.
DOI : 10.2307/2290332

J. E. Chacón, T. Duong, and M. P. Wand, Asymptotics for general multivariate kernel density derivative estimators, Statistica Sinica, vol.21, issue.2, pp.807-840, 2011.
DOI : 10.5705/ss.2011.036a

S. X. Chen, Beta kernel estimators for density functions, Computational Statistics & Data Analysis, vol.31, issue.2, pp.131-145, 1999.
DOI : 10.1016/S0167-9473(99)00010-9

S. X. Chen, Probability Density Function Estimation Using Gamma Kernels, Annals of the Institute of Statistical Mathematics, vol.52, issue.3, pp.471-480, 2000.
DOI : 10.1023/A:1004165218295

S. X. Chen, Beta kernels smoothers for regression curves, Statistica Sinica, vol.52, pp.73-91, 2000.

D. B. Cline and J. D. Hart, Kernel Estimation of Densities with Discontinuities or Discontinuous Derivatives, Statistics, vol.43, issue.1, 1991.
DOI : 10.1007/BF02481114

L. Cohen, Probability distributions with given multivariate marginals, Journal of Mathematical Physics, vol.84, issue.8, pp.2402-2403, 1984.
DOI : 10.1063/1.524501

F. Cribari-neto and A. Zeilis, Beta regression in R, Journal of Statistical Software, vol.34, pp.1-24, 2010.

S. Dabo-niang and A. Yao, Kernel spatial density estimation in infinite dimension space, Metrika, vol.8, issue.2, pp.19-52, 2013.
DOI : 10.1111/j.1467-9892.1987.tb00435.x

URL : https://hal.archives-ouvertes.fr/hal-00955728

A. Daouia, L. Gardes, and S. Girard, On kernel smoothing for extremal quantile regression, Bernoulli, vol.19, issue.5B, pp.2557-2589, 2013.
DOI : 10.3150/12-BEJ466

URL : https://hal.archives-ouvertes.fr/hal-00803127

T. Duong, Bandwidth Selectors for Multivariate Kernel Density Estimation, 2004.

V. A. Epanechnikov, Nonparametric estimation of a multivariate probability density, Theory of Probability and Its Applications 14, pp.153-158, 1969.

B. Funke and R. Kawka, Nonparametric density estimation for multivariate bounded data using two non-negative multiplicative bias correction methods, Computational Statistics & Data Analysis, vol.92, pp.148-162, 2015.
DOI : 10.1016/j.csda.2015.07.006

T. Gasser and H. G. Müller, Kernel estimation of regression functions, Smoothing techniques for curve estimation Proceedings of Workshop, 1979.
DOI : 10.1214/aoms/1177693050

T. Gasser, H. G. Müller, and V. Mammitzsch, Kernels for nonparametric curve estimation, Journal of the Royal Statistical Society, vol.2, pp.238-252, 1985.

S. Girard, A. Guillou, and G. Stupfler, Frontier estimation with kernel regression on high order moments, Journal of Multivariate Analysis, vol.116, pp.172-189, 2013.
DOI : 10.1016/j.jmva.2012.12.001

URL : https://hal.archives-ouvertes.fr/hal-00499369

A. K. Gosh and P. Chaudhury, Optimal smoothing in kernel analysis discriminant, Statistica Sinica, vol.14, pp.457-483, 2004.

A. K. Gosh and P. Hall, On error-rate estimation in nonparametric classification, Statistica Sinica, vol.18, pp.1081-1100, 2008.

W. González-manteiga, M. J. Lombardía, M. D. Martínez-miranda, and S. Sperlich, Kernel smoothers and bootstrapping for semiparametric mixed effects models, Journal of Multivariate Analysis, vol.114, pp.288-302, 2013.
DOI : 10.1016/j.jmva.2012.08.005

C. Gu, Smoothing Spline Density Estimation: A Dimensionless Automatic Algorithm, Journal of the American Statistical Association, vol.59, issue.422, pp.495-504, 1993.
DOI : 10.1090/conm/059/870445

J. D. Habbema, J. Hermans, and K. Vanden-broee, A stepwise discriminant analysis program using density estimation, Proceedings in Computationnal Statistics, pp.101-110, 1974.

P. Hall and K. Kang, Bandwidth choice for nonparametric classification, The Annals of Statistics, vol.33, issue.1, pp.284-306, 2005.
DOI : 10.1214/009053604000000959

P. Hall and M. P. Wand, On nonparametric discrimination using density differences, Biometrika, vol.75, issue.3, pp.541-547, 1988.
DOI : 10.1093/biomet/75.3.541

T. Hayfield and J. S. Racine, Nonparametric econometrics : the np package, Journal of Statistical Software, vol.27, pp.1-32, 2007.

M. L. Hazelton and J. C. Marshall, Linear boundary kernels for bivariate density estimation, Statistics & Probability Letters, vol.79, issue.8, pp.999-1003, 2009.
DOI : 10.1016/j.spl.2008.12.003

W. Härdle and J. S. James, Optimal Bandwidth Selection in Nonparametric Regression Function Estimation, The Annals of Statistics, vol.13, issue.4, pp.1465-1481, 1985.
DOI : 10.1214/aos/1176349748

J. He, G. Yang, H. Rao, Z. Li, X. Ding et al., Prediction of human major histocompatibility complex class II binding peptides by continuous kernel discrimination method, Artificial Intelligence in Medicine, vol.55, issue.2, pp.107-115, 2012.
DOI : 10.1016/j.artmed.2011.10.005

H. V. Henderson and S. R. Searle, Vec and vech operators for matrices, with some uses in jacobians and multivariate statistics, Canadian Journal of Statistics, vol.14, issue.5697, pp.65-81, 1979.
DOI : 10.1016/B978-0-12-204750-3.50019-8

M. Sobom, A. Somé-hernández-bastida, and M. P. Fernández-sanchez, A Sarmanov family with beta and gamma marginal distributions : an application to the Bayes premium in a collective risk model, Statistical Methods & Applications, vol.46, issue.21, pp.391-409, 2012.

R. Hielscher, Kernel density estimation on the rotation group and its application to crystallographic texture analysis, Journal of Multivariate Analysis, vol.119, pp.119-143, 2013.
DOI : 10.1016/j.jmva.2013.03.014

S. Hilger, Analysis on Measure Chains ??? A Unified Approach to Continuous and Discrete Calculus, Results in Mathematics, vol.14, issue.1-2, pp.18-56, 1990.
DOI : 10.1115/1.3662605

S. Hilger, Ein Maettenkalkl mit Anwendung auf Zentrumsmannigfal-tigkeiten, 1998.

M. Hirukawa and M. Sakudo, Nonnegative bias reduction methods for density estimation using asymmetric kernels, Computational Statistics & Data Analysis, vol.75, pp.112-123, 2014.
DOI : 10.1016/j.csda.2014.01.012

W. Hoeffding, Probability Inequalities for Sums of Bounded Random Variables, Journal of the American Statistical Association, vol.1, issue.301, pp.13-30, 1963.
DOI : 10.1007/BF02883985

T. Ichimura and D. Fukuda, A fast algorithm for computing least-squares cross-validations for nonparametric conditional kernel density functions, Computational Statistics & Data Analysis, vol.54, issue.12, pp.3404-3410, 2010.
DOI : 10.1016/j.csda.2009.08.021

G. Igarashi and Y. Kakizawa, Re-formulation of inverse Gaussian, reciprocal inverse Gaussian, and Birnbaum???Saunders kernel estimators, Statistics & Probability Letters, vol.84, pp.235-246, 2014.
DOI : 10.1016/j.spl.2013.10.013

G. Igarashi and Y. Kakizawa, Bias corrections for some asymmetric kernel estimators, Journal of Statistical Planning and Inference, vol.159, pp.37-63, 2015.
DOI : 10.1016/j.jspi.2014.11.003

N. L. Johnson, S. Kotz, and N. Balakrishnan, Discrete Multivariate Distributions, 1997.

B. Jørgensen, The Theory of Dispersion Models, 1997.

B. Jørgensen, Construction of multivariate dispersion models, Brazilian Journal of Probability and Statistics, vol.27, issue.3, pp.285-309, 2013.
DOI : 10.1214/11-BJPS171

B. Jørgensen and C. C. Kokonendji, Dispersion models for geometric sums, Brazilian Journal of Probability and Statistics, vol.25, issue.3, pp.263-293, 2011.
DOI : 10.1214/10-BJPS136

B. Jørgensen and C. C. Kokonendji, Discrete dispersion models and their Tweedie asymptotics, AStA Advances in Statistical Analysis, 2015.

J. Klemelä and M. C. Ripley, regpro : Nonparametric Regression, URL http://cran.r-project, 1995.

C. C. Kokonendji, Over-and Underdispersion Models In The Wiley Encyclopedia of Clinical Trials -Methods and Applications of, Planning, Analysis, and Inferential Methods, p.5066526, 2014.

C. C. Kokonendji and T. Senga-kiessé, Discrete associated kernels method and extensions, Statistical Methodology, vol.8, issue.6, pp.497-516, 2011.
DOI : 10.1016/j.stamet.2011.07.002

URL : https://hal.archives-ouvertes.fr/hal-00949369

C. C. Kokonendji, T. Senga-kiessé, and N. Balakrishnan, Semiparametric estimation for count data through weighted distributions, Journal of Statistical Planning and Inference, vol.139, issue.10, pp.3625-3638, 2009.
DOI : 10.1016/j.jspi.2009.04.013

URL : https://hal.archives-ouvertes.fr/hal-00473041

C. C. Kokonendji, T. Senga-kiessé, and C. G. Demétrio, Appropriate kernel regression on a count explanatory variable and applications, Advances and Applications in Statistics, vol.12, pp.99-125, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00952365

C. C. Kokonendji, T. Senga-kiessé, and S. S. Zocchi, Discrete triangular distributions and non-parametric estimation for probability mass function, Journal of Nonparametric Statistics, vol.71, issue.6-8, pp.241-254, 2007.
DOI : 10.1214/aos/1176350258

URL : https://hal.archives-ouvertes.fr/hal-00947709

C. C. Kokonendji and S. M. Somé, On multivariate associated kernels for smoothing some density function, 2015.

C. C. Kokonendji and D. Varron, Performance of discrete associated kernel estimators through the total variation distance, Statistics & Probability Letters, vol.110, 2015.
DOI : 10.1016/j.spl.2015.10.008

C. C. Kokonendji and S. S. Zocchi, Extensions of discrete triangular distributions and boundary bias in kernel estimation for discrete functions, Statistics & Probability Letters, vol.80, issue.21-22, pp.1655-1662, 2010.
DOI : 10.1016/j.spl.2010.07.008

S. Kotz, N. Balakrishnan, and L. N. Johnson, Continuous Multivariate Distributions, 2000.
DOI : 10.1002/0471722065

D. Kundu, N. Balakrishnan, and A. Jamalizadeh, Bivariate Birnbaum???Saunders distribution and associated inference, Journal of Multivariate Analysis, vol.101, issue.1, pp.113-125, 2010.
DOI : 10.1016/j.jmva.2009.05.005

C. N. Kuruwita, K. B. Kulasekera, and W. J. Padgett, Density estimation using asymmetric kernels and Bayes bandwidths with censored data, Journal of Statistical Planning and Inference, vol.140, issue.7, pp.1765-1774, 2010.
DOI : 10.1016/j.jspi.2010.01.001

M. T. Lee, Properties and applications of the Sarmanov family of bivariate distributions, Communications in Statistics -Theory and Methods, vol.25, pp.1207-1222, 1996.

Q. Li and J. Racine, Nonparametric Econometrics : Theory and Practice, 2007.

F. G. Libengué, Méthode Non-Paramétrique par Noyaux Associés Mixtes et Applications, French) to Université de Franche-Comté, 2013.

M. Sobom, . Somé75, F. G. Libengué, S. M. Somé, and C. C. Kokonendji, Estimation par noyaux associés mixtes d'un modèle de mélange, Actes des 45èmes Journées de Statistique de la Société Française de Statistiques (SFdS), 6pages. URL http, 2013.

B. Liu, Y. Yang, I. Webb, and J. Boughton, A comparative study of bandwidth choice in kernel density estimation for naive Bayesian classification, Advances in Knowledge Discovery and Data Mining, pp.302-313, 2012.

J. R. Magnus and H. Neudecker, Matrix Differential Calculus with Applications in Statistics and Econometrics., Biometrics, vol.44, issue.4, 1988.
DOI : 10.2307/2531754

P. Malec and M. Schienle, Nonparametric kernel density estimation near the boundary, Computational Statistics & Data Analysis, vol.72, pp.57-76, 2014.
DOI : 10.1016/j.csda.2013.10.023

N. Markovich, Nonparametric Analysis of Univariate Heavy-Tailed Data, 2008.
DOI : 10.1002/9780470723609

N. Markovich, Nonparametric Analysis of Univariate Heavy-Tailed Data, 2008.
DOI : 10.1002/9780470723609

L. C. Marsh and K. Mukhopadhyay, Discrete Poisson kernel density estimation-with an application to wildcat coal strikes, Applied Economics Letters, vol.11, issue.6, pp.393-396, 1999.
DOI : 10.2307/2171778

H. G. Müller and U. Stadtmüller, Multivariate boundary kernels and a continuous least squares principle, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.61, issue.2, pp.439-458, 1999.
DOI : 10.1111/1467-9868.00186

E. A. Nadaraya, On estimating regression, Theory of Probability and its Applications 9, pp.141-142, 1964.

E. Parzen, On Estimation of a Probability Density Function and Mode, The Annals of Mathematical Statistics, vol.33, issue.3, pp.1065-1076, 1962.
DOI : 10.1214/aoms/1177704472

R. Development and C. Team, R : A language and environment for statistical computing. R Foundation for Statistical Computing, 2015.

J. Racine, Parallel distributed kernel estimation, Computational Statistics & Data Analysis, vol.40, issue.2, pp.293-302, 2002.
DOI : 10.1016/S0167-9473(01)00109-8

B. D. Ripley, Pattern Recognition and Neural Networks, 1996.
DOI : 10.1017/CBO9780511812651

J. P. Romano and L. A. Thombs, Inference for Autocorrelations under Weak Assumptions, Journal of the American Statistical Association, vol.85, issue.434, pp.590-600, 1996.
DOI : 10.1214/aos/1176348899

M. Rosenblatt, Remarks on Some Nonparametric Estimates of a Density Function, The Annals of Mathematical Statistics, vol.27, issue.3, pp.832-837, 1956.
DOI : 10.1214/aoms/1177728190

S. R. Sain, Multivariate locally adaptive density estimation, Computational Statistics & Data Analysis, vol.39, issue.2, pp.165-186, 2002.
DOI : 10.1016/S0167-9473(01)00053-6

O. V. Sarmanov, Generalized normal correlation and two-dimensionnal Frechet classes, Doklady (Soviet Mathematics), vol.168, pp.596-599, 1966.

O. Scaillet, Density estimation using inverse and reciprocal inverse Gaussian kernels, Journal of Nonparametric Statistics, vol.78, issue.1-2, pp.217-226, 2004.
DOI : 10.1017/S0305004100023185

W. D. Scott, Multivariate Density Estimation, 1992.

E. F. Schuster, Incorporating support constraints into nonparametric estimators of densities, Communications in Statistics - Theory and Methods, vol.9, issue.5, pp.1123-1136, 1985.
DOI : 10.1080/0020739780090201

S. Kiessé and T. , Approche Non-Parametrique par Noyaux Associés Discrets des Données de Dénombrement, 2008.

B. W. Silvermann, Some aspects of the smoothing approach to nonparametric regression curve fitting, Journal of the Royal Statistical Society Series B, vol.47, pp.1-52, 1985.

B. W. Silverman, Density Estimation for Statistics and Data Analysis, 1986.
DOI : 10.1007/978-1-4899-3324-9

J. S. Simonoff, Smoothing Methods in Statistics, 1996.
DOI : 10.1007/978-1-4612-4026-6

J. S. Simonof and G. Tutz, Smoothing Methods for Discrete Data, Smoothing and Regression : Approaches, Computation, and Application, pp.193-228, 2000.
DOI : 10.1093/biomet/68.1.301

S. M. Somé and C. C. Kokonendji, Effects of associated kernels in nonparametric multiple regressions, Journal of Statistical Theory and Practice, vol.26, issue.2, 2015.
DOI : 10.1016/j.csda.2014.02.002

B. Vidakovic, Statistical Modeling by Wavelets, 1999.
DOI : 10.1002/9780470317020

G. Wahba, Splines Models for Observational Data, 1990.
DOI : 10.1137/1.9781611970128

M. P. Wand and M. C. Jones, Comparison of Smoothing Parameterizations in Bivariate Kernel Density Estimation, Journal of the American Statistical Association, vol.53, issue.422, pp.520-528, 1993.
DOI : 10.2307/2290569

M. Sobom, M. P. Somé, and M. C. Ripley, KernSmooth : Functions for Kernel Smoothing Supporting Wand Jones, URL http, 1995.

M. P. Wand and D. Ruppert, Multivariate locally weighted least squares regression, Annals of Statistics, vol.22, pp.1346-1370, 1994.

M. Wang and J. Van-ryzin, A class of smooth estimators for discrete distributions, Biometrika, vol.68, issue.1, pp.301-309, 1981.
DOI : 10.1093/biomet/68.1.301

W. E. Wansouwé, C. C. Kokonendji, and D. T. Kolyang, Disake : an R package for discrete associated kernel estimator, URL http://cran.r-project, 2015.

W. E. Wansouwé, F. G. Libengué, and C. C. Kokonendji, Conake : an R package for continuous associated kernel estimators, URL http, 2015.

W. E. Wansouwé, S. M. Somé, and C. C. Kokonendji, Ake : Associated kernel estimations, URL http://cran.r-project, 2015.

W. E. Wansouwé, S. M. Somé, and C. C. Kokonendji, Ake: an R package for discrete and continuous associated kernel estimations, 2015.

L. Wassermann, All of Nonparametrics Statistics, 2006.

G. S. Watson, Smooth regression analysis, Sankhya Series A, vol.26, pp.359-372, 1964.

I. Yahav and G. Shmueli, On generating multivariate Poisson data in management science applications, Applied Stochastic Models in Business and Industry, vol.4, issue.6, pp.91-102, 2012.
DOI : 10.1214/aos/1176343660

S. Zhang, A note on the performance of the gamma kernel estimators at the boundary, Statistics & Probability Letters, vol.80, issue.7-8, pp.548-557, 2010.
DOI : 10.1016/j.spl.2009.12.009

S. Zhang and R. J. Karunamuni, Boundary performance of the beta kernel estimators, Journal of Nonparametric Statistics, vol.53, issue.1, pp.81-104, 2010.
DOI : 10.1016/0167-9473(92)90061-J

X. Zhang, M. L. King, and H. L. Shang, A sampling algorithm for bandwidth estimation in a nonparametric regression model with a flexible error density, Computational Statistics & Data Analysis, vol.78, pp.218-234, 2014.
DOI : 10.1016/j.csda.2014.04.016

Y. Ziane, S. Adjabi, and N. Zougab, Adaptive Bayesian bandwidth selection in asymmetric kernel density estimation for nonnegative heavy-tailed data, Journal of Applied Statistics, vol.9, issue.8, pp.1645-1658, 2015.
DOI : 10.1016/j.csda.2014.02.002

N. Zougab, Approche Bayésienne dans l'Estimation Non-paramétrique de, 2013.

N. Zougab, S. Adjabi, and C. C. Kokonendji, Binomial kernel and Bayes local bandwidth in discrete function estimation, Journal of Nonparametric Statistics, vol.5, issue.3, pp.783-795, 2012.
DOI : 10.1016/j.spl.2009.12.008

N. Zougab, S. Adjabi, and C. C. Kokonendji, A Bayesian Approach to Bandwidth Selection in Univariate Associate Kernel Estimation, Journal of Statistical Theory and Practice, vol.50, issue.1, pp.8-23, 2013.
DOI : 10.1016/j.csda.2005.06.019

N. Zougab, S. Adjabi, and C. C. Kokonendji, Bayesian Approach in Nonparametric Count Regression with Binomial Kernel, Communications in Statistics - Simulation and Computation, vol.26, issue.5, pp.1052-1063, 2014.
DOI : 10.1016/j.spl.2009.12.008

N. Zougab, S. Adjabi, and C. C. Kokonendji, Bayesian estimation of adaptive bandwidth matrices in multivariate kernel density estimation, Computational Statistics & Data Analysis, vol.75, pp.28-38, 2014.
DOI : 10.1016/j.csda.2014.02.002

M. S. Sobom and . Hrp=array, length(h22))) for ( k in 1 : length(h11)){ for, p.length

. Hrp, nrow=2,ncol=2,byrow=T) } } ###################################################################### ###################################################################### CV1=function(x1,x2,V1r,V2r,Hrp,w) {b1<-1 ngr<-length(V1r) U<-array, length(Hrp[2, p.22

M. Sobom and . Somé, length(V1))) for ( r in 1 : length(h11)){ for (i in 1 :length(V1)) # boucle en i pour chaque point x[i] {for (j in 1 :length(V1)) # boucle en j pour chaque observation V, pp.1-11

*. Sum, ^2) U[r] <-F #vecteur de tous ISE selon les simulations } return(U) } ################################################# ################################################### y1<-y h1<, F<, issue.1

M. Sobom, J. Somé-references-aitchison, and C. G. Aitken, Multivariate binary discrimination by the kernel method, Biometrika, vol.63, pp.413-420, 1976.

S. X. Chen, Beta kernel estimators for density functions, Computational Statistics & Data Analysis, vol.31, issue.2, pp.131-145, 1999.
DOI : 10.1016/S0167-9473(99)00010-9

S. X. Chen, Probability Density Function Estimation Using Gamma Kernels, Annals of the Institute of Statistical Mathematics, vol.52, issue.3, pp.471-480, 2000.
DOI : 10.1023/A:1004165218295

G. Igarashi and Y. Kakizawa, Bias corrections for some asymmetric kernel estimators, Journal of Statistical Planning and Inference, vol.159, pp.37-63, 2015.
DOI : 10.1016/j.jspi.2014.11.003

C. C. Kokonendji, S. Kiessé, and T. , Discrete associated kernels method and extensions, Statistical Methodology, vol.8, issue.6, pp.497-516, 2011.
DOI : 10.1016/j.stamet.2011.07.002

URL : https://hal.archives-ouvertes.fr/hal-00949369

C. C. Kokonendji, T. Senga-kiessé, and C. G. Demétrio, Appropriate kernel regression on a count explanatory variable and applications, Advances and Applications in Statistics, vol.12, pp.99-125, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00952365

F. G. Libengue, Méthode Non-Paramétrique par Noyaux Associés Mixtes et Applications, French) to Université de Franche-Comté, 2013.

N. Zougab, S. Adjabi, and C. C. Kokonendji, Bayesian Approach in Nonparametric Count Regression with Binomial Kernel, Communications in Statistics - Simulation and Computation, vol.26, issue.5, pp.1052-1063, 2014.
DOI : 10.1016/j.spl.2009.12.008

R. Libengué and F. G. , Méthode Non-Paramétrique par Noyaux Associés Mixtes et Applications, French) to Université de Franche-Comté, 2013.

#. Examples and . Sample, V<-rgamma(100,1.5,2.6) ##The bandwidth can be the one obtained by cross validation. h<-0.052 ## We choose Gamma kernel. est<-dke.fun(V,h

M. Sobom and S. X. Somé-references-chen, Beta kernels estimators for density functions, Computational Statistics and Data Analysis, vol.31, pp.131-145, 1999.

N. Zougab, S. Adjabi, and C. C. Kokonendji, Bayesian Approach in Nonparametric Count Regression with Binomial Kernel, Communications in Statistics - Simulation and Computation, vol.26, issue.5, pp.1052-1063, 2014.
DOI : 10.1016/j.spl.2009.12.008

R. Chen and S. X. , Beta kernel estimators for density functions, Annexe : Codes sources, pp.131-145, 1999.
DOI : 10.1016/S0167-9473(99)00010-9

S. X. Chen, Probability Density Function Estimation Using Gamma Kernels, Annals of the Institute of Statistical Mathematics, vol.52, issue.3, pp.471-480, 2000.
DOI : 10.1023/A:1004165218295

F. G. Libengué, Méthode Non-Paramétrique par Noyaux Associés Mixtes et Applications, French) to Université de Franche-Comté, 2013.

G. Igarashi and Y. Kakizawa, Bias corrections for some asymmetric kernel estimators, Journal of Statistical Planning and Inference, vol.159, pp.37-63, 2015.
DOI : 10.1016/j.jspi.2014.11.003

S. X. Chen, Beta kernel estimators for density functions, Computational Statistics & Data Analysis, vol.31, issue.2, pp.131-145, 1999.
DOI : 10.1016/S0167-9473(99)00010-9

S. X. Chen, Probability Density Function Estimation Using Gamma Kernels, Annals of the Institute of Statistical Mathematics, vol.52, issue.3, pp.471-480, 2000.
DOI : 10.1023/A:1004165218295

F. G. Libengué, Méthode Non-Paramétrique par Noyaux Associés Mixtes et Applications, French) to Université de Franche-Comté, 2013.

G. Igarashi and Y. Kakizawa, Bias corrections for some asymmetric kernel estimators, Journal of Statistical Planning and Inference, vol.159, pp.37-63, 2015.
DOI : 10.1016/j.jspi.2014.11.003

M. Sobom and S. X. Somé-references-chen, Beta kernels estimators for density functions, Computational Statistics and Data Analysis, vol.31, pp.131-145, 1999.

S. X. Chen, Probability Density Function Estimation Using Gamma Kernels, Annals of the Institute of Statistical Mathematics, vol.52, issue.3, pp.471-480, 2000.
DOI : 10.1023/A:1004165218295

G. Igarashi and Y. Kakizawa, Bias corrections for some asymmetric kernel estimators, Journal of Statistical Planning and Inference, vol.159, pp.37-63, 2015.
DOI : 10.1016/j.jspi.2014.11.003

C. C. Kokonendji, S. Kiessé, and T. , Discrete associated kernels method and extensions, Statistical Methodology, vol.8, issue.6, pp.497-516, 2011.
DOI : 10.1016/j.stamet.2011.07.002

URL : https://hal.archives-ouvertes.fr/hal-00949369

C. C. Kokonendji, T. Senga-kiessé, and S. S. Zocchi, Discrete triangular distributions and non-parametric estimation for probability mass function, Journal of Nonparametric Statistics, vol.71, issue.6-8, pp.241-254, 2007.
DOI : 10.1214/aos/1176350258

URL : https://hal.archives-ouvertes.fr/hal-00947709

F. G. Libengué, Méthode Non-Paramétrique par Noyaux Associés Mixtes et Applications, French) to Université de Franche-Comté, 2013.

R. Kokonendji, C. C. , S. Kiessé, and T. , Discrete associated kernels method and extensions, Annexe : Codes sources, pp.497-516, 2011.
DOI : 10.1016/j.stamet.2011.07.002

URL : https://hal.archives-ouvertes.fr/hal-00949369

C. C. Kokonendji, T. Senga-kiessé, and S. S. Zocchi, Discrete triangular distributions and non-parametric estimation for probability mass function, Journal of Nonparametric Statistics, vol.71, issue.6-8, pp.241-254, 2007.
DOI : 10.1214/aos/1176350258

URL : https://hal.archives-ouvertes.fr/hal-00947709

N. Zougab, S. Adjabi, and C. C. Kokonendji, Binomial kernel and Bayes local bandwidth in discrete function estimation, Journal of Nonparametric Statistics, vol.5, issue.3, pp.783-795, 2012.
DOI : 10.1016/j.spl.2009.12.008

M. Sobom, C. C. Somé-references-kokonendji, S. Kiessé, and T. , Discrete associated kernel method and extensions, Statistical Methodology, vol.8, pp.497-516, 2011.

C. C. Kokonendji, T. Senga-kiessé, and S. S. Zocchi, Discrete triangular distributions and non-parametric estimation for probability mass function, Journal of Nonparametric Statistics, vol.71, issue.6-8, pp.241-254, 2007.
DOI : 10.1214/aos/1176350258

URL : https://hal.archives-ouvertes.fr/hal-00947709

N. Zougab, S. Adjabi, and C. C. Kokonendji, Binomial kernel and Bayes local bandwidth in discrete function estimation, Journal of Nonparametric Statistics, vol.5, issue.3, pp.783-795, 2012.
DOI : 10.1016/j.spl.2009.12.008

M. Sobom, C. C. Somé-references-kokonendji, S. Kiessé, and T. , Discrete associated kernel method and extensions, Statistical Methodology, vol.8, pp.497-516, 2011.

C. C. Kokonendji, T. Senga-kiessé, and S. S. Zocchi, Discrete triangular distributions and non-parametric estimation for probability mass function, Journal of Nonparametric Statistics, vol.71, issue.6-8, pp.241-254, 2007.
DOI : 10.1214/aos/1176350258

URL : https://hal.archives-ouvertes.fr/hal-00947709

N. Zougab, S. Adjabi, and C. C. Kokonendji, Binomial kernel and Bayes local bandwidth in discrete function estimation, Journal of Nonparametric Statistics, vol.5, issue.3, pp.783-795, 2012.
DOI : 10.1016/j.spl.2009.12.008