Distance Correlation Statistic and t-Test
Distance correlation t-test of multivariate and functional independence (wrapper functions of energy package).
dcor.xy(x, y, test = TRUE, metric.x, metric.y, par.metric.x, par.metric.y, n) dcor.dist(D1, D2) bcdcor.dist(D1, D2, n) dcor.test(D1, D2, n)
x |
data (fdata, matrix or data.frame class) of first sample. |
y |
data (fdata, matrix or data.frame class) of second sample. |
test |
if TRUE, compute bias corrected distance correlation statistic and the corresponding t-test, else compute distance correlation statistic. |
metric.x, metric.y |
Name of metric or semi-metric function used for
compute the distances of |
par.metric.x, par.metric.y |
List of parameters for the corresponding metric function. |
n |
The sample size used in bias corrected version of distance
correlation, by default is the number of rows of |
D1 |
Distances of first sample (x data). |
D2 |
Distances of second sample (y data). |
These wrapper functions extend the functions of the energy package
for multivariate data to functional data. Distance correlation is a measure
of dependence between random vectors introduced by Szekely, Rizzo, and
Bakirov (2007).
dcor.xy performs a nonparametric t-test of multivariate or functional
independence in high dimension. The distribution of the test statistic is
approximately Student t with n(n-3)/2-1 degrees of freedom and for
n ≥q 10 the statistic is approximately distributed as standard
normal. Wrapper function of energy:::dcor.ttest. The t statistic is
a transformation of a bias corrected version of distance correlation (see SR
2013 for details). Large values (upper tail) of the t statistic are
significant.dcor.test similar to dcor.xy but only for distance matrix.
dcor.dist compute distance correlation statistic. Wrapper function
of energy::dcor but only for distance matrix
bcdcor.dist compute bias corrected distance correlation statistic.
Wrapper function of energy:::bcdcor but only for distance matrix.
dcor.test returns a list with class htest containing
method description of test
statistic observed value of the test statistic
parameter degrees of freedom
estimate bias corrected distance correlation bcdcor(x,y)
p.value p-value of the t-test
data.name description of data
dcor.xy returns the previous list with class htest and
D1 the distance matrix of x
D2 the distance matrix of y
dcor.dist returns the distance correlation statistic.
bcdcor.dist returns the bias corrected distance correlation
statistic.
Manuel Oviedo de la Fuente manuel.oviedo@usc.es and Manuel Febrero Bande
Szekely, G.J. and Rizzo, M.L. (2013). The distance correlation t-test of independence in high dimension. Journal of Multivariate Analysis, Volume 117, pp. 193-213.
Szekely, G.J., Rizzo, M.L., and Bakirov, N.K. (2007), Measuring and Testing Dependence by Correlation of Distances, Annals of Statistics, Vol. 35 No. 6, pp. 2769-2794.
metric.lp amd metric.dist.
## Not run: x<-rproc2fdata(100,1:50) y<-rproc2fdata(100,1:50) dcor.xy(x, y,test=TRUE) dx <- metric.lp(x) dy <- metric.lp(y) dcor.test(dx, dy) bcdcor.dist(dx, dy) dcor.xy(x, y,test=FALSE) dcor.dist(dx, dy) ## End(Not run)
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