delta.test {LambertW}R Documentation

Test for significance of delta

Description

Given the simulated critical values for the GMM method and for delta=0 (see Goerg (2009)), this function performs a test on the significance an estimated delta.

Usage

delta.test(object)

Arguments

object object of class LWest

Details

If the data is truly Gaussian – hence true delta = 0 – then

frac{widehat{delta} sqrt{N}}{0.4} sim N(0,1),

where N is the sample size, and widehat{delta} is the estimated delta via GMM.

Value

A list with class "htest" containing the following components:

statistic the value of the test statistic.
p.value the p-value for the test.
method the character string "Simulation based GMM significanc test (Asymptotic Gaussian)"
data.name a character string giving the name(s) of the data.

Author(s)

Georg M. Goerg

References

Goerg, G.M. (2009). “Lambert W Random Variables - A new class of skewed distribution functions”. Unpublished

Examples

set.seed(1)
y=rnorm(1000)
fit=IGMM(y)
delta.test(fit) # not-significant because data is truly Gaussian

data(AA)
attach(AA)
X=AA[AA$sex=="f",]
y=X$bmi

fit=IGMM(y)
delta.test(fit) ### Significant delta as the data is highly skewed to the right

[Package LambertW version 0.1.6 Index]