localgauss.indtest {localgauss}

Pointwise Independence test based on local Gaussian correlation

Description

Routine for testing for local independence based on local Gaussian parameters. It accepts an S3 object produced by localgauss(), and perfoms a bootstrap-based test with null-hypothesis being that x and y are indpendent.

Usage

localgauss.indtest(locobj,R=10,alpha=0.10,seed=1)

Arguments

locobj

localgauss-object

R

Number of bootstrap replica

alpha

significance level (note: two sided test)

seed

Random seed in used for bootstrap

Details

The test is based on producing a null-distribution of local Gaussian correlations were the original data are resampled from their empirical marginal distributions. The bootstrap-based null-distribution is produced for each point specified in xy.mat in locobj. An estimated local correlation for the original data significantly larger than the null-distribution is indicated with +1 (returned in the vector test.results). An estimated local correlation for the original data insignifcant with respect to the null-distribution is indicated with 0. An estimated local correlation for the original datasignificantly smaller than the null-distribution is indicated with -1.

Value

S3 object of type localgauss.indtest containing the fields:

localgauss

simply returns locobj.

upper

Vector containing the 1-alpha/2 quantiles of the null-distributions.

lower

Vector containing the alpha/2 quantiles of the null-distributions.

test.results

Vector containing the test results.

References

Geir Drage Berentsen, Tore Selland Kleppe, Dag Tjostheim, Introducing localgauss, an R Package for Estimating and Visualizing Local Gaussian Correlation, Journal of Statistical Software, 56(12), 1-18, 2014, (http://www.jstatsoft.org/v56/i12/). Note that for compability reasons, the graphics routines described in the paper have been taken out from release 0.40. See also Tjoestheim, D. and Hufthammer K. O., Local Gaussian correlation: A new measure of dependence, Journal of Econometrics, 172(1),pages 33-48,2013, for a detailed description of local Gaussian correlation and Berentsen, G.D. and Tjoestheim D., Recognizing and visualizing departures from independence in bivariate data using local Gaussian correlation, http://people.uib.no/gbe062/local-gaussian-correlation/ for a description of the local independence test.

See Also

localgauss.

Examples

    x=rnorm(n=100)
    y=x^2 + rnorm(n=100)
    lgobj = localgauss(x,y,gsize=8)
    lgind = localgauss.indtest(lgobj)