kef {Ake}

Continuous and discrete associated kernel function

Description

This function computes the associated kernel function.

Usage

kef(x, t, h, type_data = c("discrete", "continuous"), 
ker = c("bino", "triang", "dirDU", "BE", "GA", "LN", "RIG"), 
a0 = 0, a1 = 1, a = 1, c = 2)

Arguments

x

The target.

t

A single value or the grid where the associated kernel function is computed.

h

The bandwidth or smoothing parameter.

type_data

The sample data type

ker

The associated kernel:"bino" Binomial, "triang" discrete triangular kernel, "BE" extended beta, "GA" gamma, "LN" lognormal and "RIG" reciprocal inverse Gaussian,"dirDU" DiracDU.

a0

The left bound of the support used for extended beta kernel. Default value is 0 for beta kernel.

a1

The right bound of the support used for extended beta kernel. Default value is 1 for beta kernel.

a

The arm in discrete triangular kernel. The default value is 1.

c

The number of categories in DiracDU kernel. The default value is 2.

Details

The associated kernel is one of the those which have been defined in the sections above : extended beta, gamma, lognormal, reciprocal inverse Gaussian, DiracDU, binomial and discrete triangular; see Kokonendji and Senga Kiessé (2011), and also Kokonendji et al. (2007).

Value

Returns the value of the associated kernel function at t according to the target and the bandwidth.

Author(s)

W. E. Wansouwé, S. M. Somé and C. C. Kokonendji

References

Chen, S. X. (1999). Beta kernels estimators for density functions, Computational Statistics and Data Analysis 31, 131 - 145.

Chen, S. X. (2000). Probability density function estimation using gamma kernels, Annals of the Institute of Statistical Mathematics 52, 471 - 480.

Igarashi, G. and Kakizawa, Y. (2015). Bias correction for some asymmetric kernel estimators, Journal of Statistical Planning and Inference 159, 37 - 63.

Kokonendji, C.C. and Senga Kiessé, T. (2011). Discrete associated kernel method and extensions, Statistical Methodology 8, 497 - 516.

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.

Libengué, F.G. (2013). Méthode Non-Paramétrique par Noyaux Associés Mixtes et Applications, Ph.D. Thesis Manuscript (in French) to Université de Franche-Comté, Besançon, France and Université de Ouagadougou, Burkina Faso, June 2013, LMB no. 14334, Besançon.

Examples

x<-5
h<-0.2
t<-0:10
kef(x,t,h,"discrete","bino")