It compute the Ln-statistic, from a bivariate sample of continuous random variables X and Y.
numeric vectors of data values. x and y must have the same length.
See Section 2.-Main reference.
The value of the Ln-statistic.
J. E. Garcia and V. A. Gonzalez-Lopez
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
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## 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
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