lis.test {LIStest}

Test for independence between paired samples

Description

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.

Usage

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.

Value

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.

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

# 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")
#