Description Usage Arguments Details Value Author(s) References Examples

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.

1 2 |

`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). |

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

`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. |

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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 | ```
# 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")
#
``` |

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