cvmgof (version 1.0.0)

acgm.statistics: Local test statistic for the regression function

Description

This function computes the local test statistic for the regression function.

Usage

acgm.statistics(data.X, data.Y, linkfunction.H0,
		bandwidth = "optimal",
		kernel.function = kernel.function.epan,
		integration.step = 0.01,
		verbose = TRUE)

Arguments

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.

linkfunction.H0

the regression function under the null hypothesis.

bandwidth

bandwidth used to obtain the nonparametric estimator of the regression function. If bandwidth = "optimal", the optimal bandwidth of the regression function under the null hypothesis is computed. Default option is "optimal".

kernel.function

kernel function used to obtain the nonparametric estimator of theregression function. Default option is "kernel.function.epan".

integration.step

a numeric value specifying integration step. Default is integration.step = 0.01.

verbose

If TRUE, the R function displays the optimal bandwidth value obtained under the null hypothesis. Default option is TRUE.

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 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

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

# Bandwidth selection under H0

# We want to test if the link function is f(x)=0.2*x^2-x+2
# The answer is yes (see the definition of data.Y above)
# We generate a dataset under H0 to estimate the optimal bandwidth under H0

linkfunction.H0 = function(x){0.2*x^2-x+2}

data.X.H0 = runif(n,min=0,max=5)
data.Y.H0 = linkfunction.H0(data.X.H0)+rnorm(n,mean=0,sd=0.3)

h.opt.acgm = acgm.bandwidth.selection.linkfunction(data.X.H0 , data.Y.H0,linkfunction.H0)

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

# Test statistics under H0

acgm.statistics(data.X,data.Y,linkfunction.H0,h.opt.acgm)

# }