Conake (version 1.0.1)

kef: Continuous associated kernel function

Description

This function computes the discrete associated kernel function; see Chen (1999) and also Chen (2000).

Usage

kef(x, t, h, ker, a = 0, b = 1)

Arguments

x

The target.

t

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

h

The bandwidth or smoothing parameter.

ker

The associated kernel: "BE" extended beta, "GA" gamma, "LN" lognormal and "RIG" reciprocal inverse Gaussian.

a

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

b

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

Value

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

Details

The associated kernel is one of the four which have been defined in the sections above : extended beta, gamma, lognormal and reciprocal inverse Gaussian; see Igarashi and Kakizawa (2015) and also Libengu<U+00E9> (2013).

References

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

Chen, S. X. (2000). Gamma kernels estimators for density functions, Annals of the Institute of Statistical Mathematics 52, 471 - 480.

Libengu<U+00E9>, F.G. (2013).M<U+00E9>thode Non-Param<U+00E9>trique par Noyaux Associ<U+00E9>s Mixtes et Applications, Ph.D. Thesis Manuscript (in French) to Universit<U+00E9> de Franche-Comt<U+00E9>, Besan<U+00E7>on, France and Universit<U+00E9> de Ouagadougou, Burkina Faso, June 2013, LMB no. 14334, Besan<U+00E7>on.

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

Examples

# NOT RUN {
x<-4
h<-0.1
t<-0:10
kef(x,t,h,"GA")

# }