acgm.linkfunction.estim {cvmgof}R Documentation

Local linear estimation of the regression function

Description

This function computes the local linear estimation of the regression function.

Usage

acgm.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 regression function.

data.Y

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

bandwidth

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

kernel.function

kernel function used to obtain the nonparametric 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.

Author(s)

Romain Azais, Sandie Ferrigno and Marie-Jose Martinez

References

J. T. Alcala, J. A. Cristobal, and W. Gonzalez Manteiga. Goodness-of-fit test for linear models based on local polynomials. Statistics & Probability Letters, 42(1), 39:46, 1999.

R. Azais, S. Ferrigno and M-J Martinez. cvmgof: An R package for Cramér-von Mises goodness-of-fit tests in regression models. 2018. Preprint in progress.

Examples

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_acgm = acgm.linkfunction.estim(xgrid,data.X,data.Y,bandwidth)

plot(xgrid,ygrid_acgm,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')


[Package cvmgof version 1.0.0 Index]