cvmgof (version 1.0.0)

vkgmss.sd.estim: Kernel estimation of the standard deviation function

Description

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)

# }