# Test for independence between paired samples Test for independence between X and Y computed from a paired sample (x1,y1),...(xn,yn) of (X,Y), using one of the following statistics (a) the Longest Increasing Subsequence (Ln), (b) JLn, a Jackknife version of Ln or (c) JLMn, a Jackknife version of the longest monotonic subsequence. This family of tests can be applied under the assumption of continuity of X and Y. ```r lis.test(x, y, alternative = c("two.sided", "less", "greater"), method = c("JLMn", "Ln", "JLn")) ``` ## Arguments - `x, y`: numeric vectors of data values. x and y must have the same length. - `alternative`: indicates the alternative hypothesis and must be one of "two.sided"(default), "greater" or "less". - `method`: a character string indicating which statistics is to be used for the test. One of "Ln", "JLn", or "JLMn"(default). ## Details For sample sizes less than 20, the correction introduced in subsection 3.2 from main reference, with c = 0.4 was avoided. ## Returns - **sample.estimate**: the value of the statistic. - **p.value**: the p-value for the test. - **alternative**: a character string describing the alternative hypothesis. - **method**: a character string indicating what type of Lis-test was performed. ## 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](http://dx.doi.org/10.1016/j.jmva.2014.02.010) ## Author(s) J. E. Garcia and V. A. Gonzalez-Lopez ## Examples ```r # Example 1 # 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 p.value using the default settings (method="JLMn" # and alternative="two.sided") lis.test(X1,X2) # calculate the p.value using method="JLn" and # alternative="two.sided". lis.test(X1,X2,method="JLn") # # Example 2: see subsection 4.3.2-Application 2 from main reference. # (It requires the package VGAM) # #require(VGAM) #plot(coalminers$BW, coalminers$nBW) #lis.test(coalminers$BW, coalminers$nBW, #alternative = "greater", method = "Ln") #lis.test(coalminers$BW, coalminers$nBW, #alternative = "greater", method = "JLn") # ```

lis.test function