vkgmss.sd.estim
Kernel estimation of the standard deviation function
This function computes the kernel (Nadaraya-Watson) estimation of the standard deviation function.
Usage
vkgmss.sd.estim(x, data.X, data.Y, bandwidth,
kernel.function = kernel.function.epan)Arguments
- x
a numeric vector.
- data.X
a numeric data vector used to obtain the kernel estimator of the standard deviation function.
- data.Y
a numeric data vector used to obtain the kernel estimator of the standard deviation function.
- bandwidth
bandwidth used to obtain the kernel estimator of the standard deviation function.
- kernel.function
kernel function used to obtain the kernel estimator of the standard deviation 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 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
# 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 residuals standard deviation
bandwidth = 0.75 # Here, the bandwidth is arbitrarily fixed
xgrid = seq(0,5,by=0.1)
sd = vkgmss.sd.estim(xgrid,data.X,data.Y,bandwidth)
plot(xgrid,sd , type='l',xlab='X',ylab='SD(X)')
abline(h=0.3)
# }