reg.fun: Function for associated kernel estimation of regression

In Ake: Associated Kernel Estimations

Function for associated kernel estimation of regression

Description

The function estimates the discrete and continuous regression in a single value or in a grid using associated kernels. Different associated kernels are available: extended beta, gamma, lognormal, reciprocal inverse Gaussian (for continuous data), DiracDU (for categorical data), binomial and also discrete triangular (for count data).

Usage

reg.fun(Vec, ...)
## Default S3 method:
reg.fun(Vec, y, type_data = c("discrete", "continuous"), 
ker = c("bino", "triang", "dirDU", "BE", "GA", "LN", "RIG"),
 h, x = NULL, a0 = 0, a1 = 1, a = 1, c = 2, ...)

Arguments

Vec	The explanatory variable.
y	The response variable.
type_data	The sample data type.
ker	The associated kernel: "dirDU" DiracDU,"bino" binomial, "triang" discrete triangular, etc.
h	The bandwidth or smoothing parameter.
x	The single value or the grid where the regression is computed.
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 0 for beta kernel.
a	The arm in Discrete Triangular kernel. The default value is 1.
c	The number of categories in DiracDU. The default value is 2.
...	Further arguments

Details

The associated kernel estimator \widehat{m}_n of m is defined in the above sections; see also Kokonendji and Senga Kiessé (2011). The bandwidth parameter in the function is obtained using the cross-validation technique for the seven associated kernels. For binomial kernel, the local Bayesian approach is also implemented; see Zougab et al. (2014).

Value

Returns a list containing:

data	The data sample, explanatory variable
y	The data sample, response variable
n	The size of the sample
kernel	The asociated kernel
h	The bandwidth
eval.points	The grid where the regression is computed
m_n	The estimated values
Coef_det	The coefficient of determination

Author(s)

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

References

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 Demétrio, C.G.B. (2009). Appropriate kernel regression on a count explanatory variable and applications, Advances and Applications in Statistics 12, 99 - 125.

Zougab, N., Adjabi, S. and Kokonendji, C.C. (2014). Bayesian approach in nonparametric count regression with binomial kernel, Communications in Statistics - Simulation and Computation 43, 1052 - 1063.

Examples

data(milk)
x=milk$week
y=milk$yield
##The bandwidth is the one obtained by cross validation.
h<-0.10
## We choose binomial kernel.
## Not run: 
m_n<-reg.fun(x, y, "discrete",ker="bino", h)

## End(Not run)

Ake documentation built on June 13, 2022, 5:07 p.m.