fEqMoments.test: Tests for checking the equality of means and/or covariance... In fda.usc: Functional Data Analysis and Utilities for Statistical Computing

 fEqMoments.test R Documentation

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 manuel.febrero@usc.es

References

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

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.