df.statistics {cvmgof}

Global test statistic for the conditional distribution function

Description

This function computes the global test statistic for the conditional distribution function.

Usage

df.statistics(data.X, data.Y, cdf.H0, bandwidth,
    kernel.function = kernel.function.epan, integration.step = 0.01)

Arguments

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.

cdf.H0

the conditional distribution function under the null hypothesis.

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".

integration.step

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

Details

An inappropriate bandwidth choice can produce "NaN" values in cumulative distribution function estimates.

Author(s)

Romain Azais, Sandie Ferrigno and Marie-Jose Martinez

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 Cramer-von Mises goodness-of-fit tests in regression models. Submitted. January 2021.hal-03101612

Examples

# Uncomment the following code block
#
# 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.df = df.bandwidth.selection.linkfunction(data.X.H0, data.Y.H0,linkfunction.H0)
#
# ########################################################################
#
# # Test statistics under H0
#
# cond_cdf.H0 = function(x,y)
# {
#   out=matrix(0,nrow=length(x),ncol=length(y))
#   for (i in 1:length(x)){
#     x0=x[i]
#     out[i,]=pnorm(y-linkfunction.H0(x0),0,0.3)
#   }
#   out
# }
# # cond_cdf.H0 is the conditional CDF associated with linkfunction.H0
# # with additive Gaussian noise (standard deviation=0.3)
#
# df.statistics(data.X,data.Y,cond_cdf.H0,h.opt.df)