vkgmss.linkfunction.estim: Kernel estimation of the regression function

Description

This function computes the kernel (Nadaraya-Watson) estimation of the regression function.

Usage

vkgmss.linkfunction.estim(x, data.X, data.Y, bandwidth,
		kernel.function = kernel.function.epan)

Arguments

a numeric vector.

data.X

a numeric data vector used to obtain the kernel estimator of the regression function.

data.Y

a numeric data vector used to obtain the kernel estimator of the regression function.

bandwidth

bandwidth used to obtain the kernel estimator of the regression function.

kernel.function

kernel function used to obtain the kernel estimator of the regression function. Default option is "kernel.function.epan" which corresponds to the Epanechnikov kernel function.

Details

Inappropriate bandwidth or x choices can produce "NaN" values in link function estimates.

References

I. Van Keilegom, W. Gonzalez Manteiga, and C. Sanchez Sellero. Goodness-of-fit tests in parametric regression based on the estimation of the error distribution. Test, 17, 401:415, 2008.

R. Azais, S. Ferrigno and M-J Martinez. cvmgof: An R package for Cram<U+00E9>r-von Mises goodness-of-fit tests in regression models. 2018. Preprint in progress.

Examples

Run this code

# NOT RUN {
set.seed(1)

# Data simulation
n = 25 # Dataset size
data.X = runif(n,min=0,max=5) # X
data.Y = 0.2*data.X^2-data.X+2+rnorm(n,mean=0,sd=0.3) # Y

########################################################################

# Estimation of the link function

bandwidth = 0.75 # Here, the bandwidth is arbitrarily fixed

xgrid = seq(0,5,by=0.1)
ygrid_vkgmss = vkgmss.linkfunction.estim(xgrid,data.X,data.Y,bandwidth)

plot(xgrid,ygrid_vkgmss,type='l',lty=1,lwd=2,xlab='X',ylab='Y',ylim=c(0.25,2.5))
lines(xgrid,0.2*xgrid^2-xgrid+2,lwd=0.5,col='gray')

# }

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