# JLMn: JLMn statistic, to test independence In LIStest: Tests of independence based on the Longest Increasing Subsequence

## Description

It compute the JLMn-statistic, from a bivariate sample of continuous random variables X and Y.

## Usage

 `1` ```JLMn(x, y) ```

## Arguments

 `x, y` numeric vectors of data values. x and y must have the same length.

## Details

See subsection 3.3-Main reference. For sample sizes less than 20, the correction introduced in subsection 3.2 from main reference, with c = 0.4 was avoided.

## Value

The value of the JLMn-statistic.

## Author(s)

J. E. Garcia, V. A. Gonzalez-Lopez

## References

J. E. Garcia, V. A. Gonzalez-Lopez, Independence tests for continuous random variables based on the longest increasing subsequence, Journal of Multivariate Analysis (2014), http://dx.doi.org/10.1016/j.jmva.2014.02.010

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```# mixture of two bivariate normal, one with correlation 0.9 and # the other with correlation -0.9 # N <-100 ro<- 0.90 Z1<-rnorm(N) Z2<-rnorm(N) X2<-X1<-Z1 I<-(1:floor(N*0.5)) I2<-((floor(N*0.5)+1):N) X1[I]<-Z1[I] X2[I]<-(Z1[I]*ro+Z2[I]*sqrt(1-ro*ro)) X1[I2]<-Z1[I2] X2[I2]<-(Z1[I2]*(-ro)+Z2[I2]*sqrt(1-ro*ro)) plot(X1,X2) #calculate the statistic a<-JLMn(X1,X2) a ```

LIStest documentation built on May 30, 2017, 3:32 a.m.