# fEqDistrib.test: Tests for checking the equality of distributions between two... In fda.usc: Functional Data Analysis and Utilities for Statistical Computing

 fEqDistrib.test R Documentation

## Tests for checking the equality of distributions between two functional populations.

### Description

Three tests for the equality of distributions of two populations are provided. The null hypothesis is that the two populations are the same

### Usage

```XYRP.test(X.fdata, Y.fdata, nproj = 10, npc = 5, test = c("KS", "AD"))

MMD.test(
X.fdata,
Y.fdata,
metric = "metric.lp",
B = 1000,
alpha = 0.95,
kern = "RBF",
ops.metric = list(lp = 2),
draw = FALSE
)

MMDA.test(
X.fdata,
Y.fdata,
metric = "metric.lp",
B = 1000,
alpha = 0.95,
kern = "RBF",
ops.metric = list(lp = 2),
draw = FALSE
)

fEqDistrib.test(
X.fdata,
Y.fdata,
metric = "metric.lp",
method = c("Exch", "WildB"),
B = 5000,
ops.metric = list(lp = 2),
iboot = FALSE
)
```

### Arguments

 `X.fdata` `fdata` object containing the curves from the first population. `Y.fdata` `fdata` object containing the curves from the second population. `nproj` Number of projections for `XYRP.test`. `npc` The number of principal components employed for generating the random projections. `test` For `XYRP.test` "KS" and/or "AD" for computing Kolmogorov-Smirnov or Anderson-Darling p-values in the projections. `metric` Character with the metric function for computing distances among curves. `B` Number of bootstrap or Monte Carlo replicas. `alpha` Confidence level for computing the threshold. By default =0.95. `kern` For `MMDA.test` "RBF" or "metric" for indicating the use of Radial Basis Function or directly, the distances. `ops.metric` List of parameters to be used with `metric`. `draw` By default, FALSE. Plots the density of the bootstrap replicas jointly with the statistic. `method` In `fEqDistrib.test` a character indicating the bootstrap method for computing the distribution under H0. "Exch" for Exchangeable bootstrap and "WildB" for Wild Bootstrap. By default, both are provided. `iboot` In `fEqDistrib.test` returns the bootstrap replicas.

### Details

`XYRP.test` computes the p-values using random projections. Requires `kSamples` library. `MMD.test` computes Maximum Mean Discrepancy p-values using permutations (see Sejdinovic et al, (2013)) and `MMDA.test` does the same using an asymptotic approximation. `fEqDistrib.test` checks the equality of distributions using an embedding in a RKHS and two bootstrap approximations for calibration.

### Value

A list with the following components by function:

• `XYRP.test`: `FDR.pv`: p-value using FDR, `proj.pv`: Matrix of p-values obtained for projections.

• `MMD.test`,`MMDA.test`: `stat`: Statistic, `p.value`: p-value, `thresh`: Threshold at level `alpha`.

• `fEqDistrib.test`: `result`: `data.frame` with columns `Stat` and `p.value`, `Boot`: `data.frame` with bootstrap replicas if `iboot=TRUE`.

### Author(s)

Manuel Febrero-Bande, Manuel Oviedo de la Fuente manuel.febrero@usc.es

### References

Sejdinovic, D., Sriperumbudur, B., Gretton, A., Fukumizu, K. Equivalence of distance-based and RKHS-based statistics in Hypothesis Testing The Annals of Statistics, 2013. DOI 10.1214/13-AOS1140.

`fmean.test.fdata, cov.test.fdata`.

### 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)
XYRP.test(X,Y,nproj=15)
MMD.test(X,Y,B=1000)
fEqDistrib.test(X,Y,B=1000)

## End(Not run)

```

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