cvmgof (version 1.0.0)

df.linkfunction.estim: Local linear estimation of the regression function

Description

This function computes the local linear estimation of the regression function using the local linear estimation of the conditional distribution function.

Usage

df.linkfunction.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 nonparametric estimator of the conditional distribution function.

data.Y

a numeric data vector used to obtain the nonparametric estimator of the conditional distribution function.

bandwidth

bandwidth used to obtain the nonparametric estimator of the conditional distribution function.

kernel.function

kernel function used to obtain the nonparametric estimator of the conditional distribution 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

G. R. Ducharme and S. Ferrigno. An omnibus test of goodness-of-fit for conditional distributions with applications to regression models. Journal of Statistical Planning and Inference, 142, 2748:2761, 2012.

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 the link function

bandwidth = 0.75 # Here, the bandwidth is arbitrarily fixed

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

plot(xgrid,ygrid_df,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')

# }