gof.sandwich {EDFtest}

GOF tests for general distributions using Sandwich estimation of covariance function

Description

This function tests the hypothesis that data y come from distribution Fdist with unknown parameter values theta. Estimates of theta must be provided in thetahat.

Usage

gof.sandwich(y, x = NULL, Fdist, thetahat, Score, m = max(n, 100), ...)

Arguments

y

A random sample or the response of regression problem.

x

The matrix of covariates.

Fdist

User supplied function to compute probability integral transform of y.

thetahat

Parameter estimates by MLE.

Score

User supplied function to compute 3 components of the score function an n by p matrix with entries partial log f(y_i,\theta)/ partial theta_j.

m

Eigenvalues are extracted for an m by m grid of the covariance function.

...

Other inputs passed to Fdist and Score when needed.

Details

It uses a large sample approximation to the limit distribution based on the use of the score function components to estimate the Fisher information and the limiting covariance function of the empirical process.

The estimates thetahat should be roots of the likelihood equations.

Value

Cramér-von Mises, Anderson-Darling and Watson statistics and their P-values.

See Also

gof for generic functions using imhof function; gof.bootstrap for generic functions using bootstrap method.

Examples

sample = rnorm(n=100,mean=0,sd=1)
mle = estimate.normal(sample)
cdf.normal.user = function(x,theta){
 pnorm(x,mean=theta[1],sd=theta[2])
}
score.normal.user = function(x,theta){
 sig=theta[2]
 mu=theta[1]
 s.mean= (x-mu)/sig
 s.sd= s.mean^2/sig-length(x)/sig
 cbind(s.mean/sig,s.sd)
}
output = gof.sandwich(y=sample,Fdist=cdf.normal.user,thetahat=mle,Score=score.normal.user,m=100)
output