Ln {LIStest}

Ln (Longest Increasing Subsequence) statistic, to test independence

Description

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

Usage

Ln(x, y)

Arguments

x, y

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

Details

See Section 2.-Main reference.

Value

The value of the Ln-statistic.

Author(s)

J. E. Garcia and 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

## 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<-Ln(X1,X2)
a