df.statistics: 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.

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

Run this code

# 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.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)

# }

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