fEqMoments.test: Tests for checking the equality of means and/or covariance...

In fda.usc: Functional Data Analysis and Utilities for Statistical Computing

Tests for checking the equality of means and/or covariance between two populations under gaussianity.

Description

Two tests for the equality of means and covariances of two populations are provided. Both tests are constructed under gaussianity following Horvath & Kokoszka, 2012, Chapter 5.

Usage

fmean.test.fdata(
  X.fdata,
  Y.fdata,
  method = c("X2", "Boot"),
  npc = 5,
  alpha = 0.95,
  B = 1000,
  draw = FALSE
)

cov.test.fdata(
  X.fdata,
  Y.fdata,
  method = c("X2", "Boot"),
  npc = 5,
  alpha = 0.95,
  B = 1000,
  draw = FALSE
)

Arguments

X.fdata	fdata object containing the curves from the first population.
Y.fdata	fdata object containing the curves from the second population.
method	c("X2","Boot"). "X2" includes the asymptotic distribution. "Boot" computes the bootstrap approximation.
npc	The number of principal components employed. If npc is negative and 0<abs(npc)<1, the number of components are determined for explaining, at least, abs(p)% of variability.
alpha	Confidence level. By default =0.95.
B	Number of bootstrap replicas when method="Boot".
draw	By default, FALSE. Plots the density of the bootstrap replicas jointly with the statistic.

Details

fmean.test.fdata computes the test for equality of means. cov.test.fdata computes the test for equality of covariance operators. Both tests have asymptotic distributions under the null related with chi-square distribution. Also, a parametric bootstrap procedure is implemented in both cases.

Value

Return a list with:

• stat Value of the statistic.

• pvalue P-values for the test.

• vcrit Critical cutoff for rejecting the null hypothesis.

• p Degrees of freedom for X2 statistic.

• B Number of bootstrap replicas.

Author(s)

Manuel Febrero-Bande, Manuel Oviedo de la Fuente [e-mail]

References

Inference for Functional Data with Applications. Horvath, L and Kokoszka, P. (2012). Springer.

See Also

See Also as fanova.RPm, fanova.onefactor.

Examples

## Not run: 
tt=seq(0,1,len=51)
bet=0
mu1=fdata(10*tt*(1-tt)^(1+bet),tt)
mu2=fdata(10*tt^(1+bet)*(1-tt),tt) 
fsig=1
X=rproc2fdata(100,tt,mu1,sigma="vexponential",par.list=list(scale=0.2,theta=0.35))
Y=rproc2fdata(100,tt,mu2,sigma="vexponential",par.list=list(scale=0.2*fsig,theta=0.35))
fmean.test.fdata(X,Y,npc=-.98,draw=TRUE)
cov.test.fdata(X,Y,npc=5,draw=TRUE)
bet=0.1
mu1=fdata(10*tt*(1-tt)^(1+bet),tt)
mu2=fdata(10*tt^(1+bet)*(1-tt),tt) 
fsig=1.5
X=rproc2fdata(100,tt,mu1,sigma="vexponential",par.list=list(scale=0.2,theta=0.35))
Y=rproc2fdata(100,tt,mu2,sigma="vexponential",par.list=list(scale=0.2*fsig,theta=0.35))
fmean.test.fdata(X,Y,npc=-.98,draw=TRUE)
cov.test.fdata(X,Y,npc=5,draw=TRUE)

## End(Not run)

fda.usc documentation built on Oct. 17, 2022, 9:06 a.m.