gSeg (version 1.0)

gseg1: Graph-Based Change-Point Detection for Single Change-Point

Description

This function finds a break point in the sequence where the underlying distribution changes. It provides four graph-based test statistics.

Usage

gseg1(n, E, statistics=c("all","o","w","g","m"), n0=0.05*n, n1=0.95*n, pval.appr=TRUE,
 skew.corr=TRUE, pval.perm=FALSE, B=100)

Arguments

n

The number of observations in the sequence.

E

The edge matrix (a "number of edges" by 2 matrix) for the similarity graph. Each row contains the node indices of an edge.

statistics

The scan statistic to be computed. A character indicating the type of of scan statistic desired. The default is "all".

"all": specifies to compute all of the scan statistics: original, weighted, generalized, and max-type;

"o", "ori" or "original": specifies the original edge-count scan statistic;

"w" or "weighted": specifies the weighted edge-count scan statistic;

"g" or "generalized": specifies the generalized edge-count scan statistic; and

"m" or "max": specifies the max-type edge-count scan statistic.

n0

The starting index to be considered as a candidate for the change-point.

n1

The ending index to be considered as a candidate for the change-point.

pval.appr

If it is TRUE, the function outputs p-value approximation based on asymptotic properties.

skew.corr

This argument is useful only when pval.appr=TRUE. If skew.corr is TRUE, the p-value approximation would incorporate skewness correction.

pval.perm

If it is TRUE, the function outputs p-value from doing B permutations, where B is another argument that you can specify. Doing permutation could be time consuming, so use this argument with caution as it may take a long time to finish the permutation.

B

This argument is useful only when pval.perm=TRUE. The default value for B is 100.

Value

Returns a list scanZ with tauhat, Zmax, and a vector of the scan statistics for each type of scan statistic specified. See below for more details.

tauhat

An estimate of the location of the change-point.

Zmax

The test statistic (maximum of the scan statistics).

Z

A vector of the original scan statistics (standardized counts) if statistic specified is "all" or "o".

Zw

A vector of the weighted scan statistics (standardized counts) if statistic specified is "all" or "w".

S

A vector of the generalized scan statistics (standardized counts) if statistic specified is "all" or "g".

M

A vector of the max-type scan statistics (standardized counts) if statistic specified is "all" or "m".

R

A vector of raw counts of the original scan statistic. This output only exists if the statistic specified is "all" or "o".

Rw

A vector of raw counts of the weighted scan statistic. This output only exists if statistic specified is "all" or "w".

pval.appr

The approximated p-value based on asymptotic theory for each type of statistic specified.

pval.perm

This output exists only when the argument pval.perm is TRUE . It is the permutation p-value from B permutations and appears for each type of statistic specified (same for perm.curve, perm.maxZs, and perm.Z).

perm.curve

A B by 2 matrix with the first column being critical values corresponding to the p-values in the second column.

perm.maxZs

A sorted vector recording the test statistics in the B permutaitons.

perm.Z

A B by n matrix with each row being the scan statistics from each permutaiton run.

See Also

gSeg, gseg2, gseg1_discrete

Examples

# NOT RUN {
data(Example)
# Five examples, each example is a n-length sequence.
# Ei (i=1,...,5): an edge matrix representing a similarity graph constructed on the
# observations in the ith sequence.  
# Check '?gSeg' to see how the Ei's were constructed.


## E1 is an edge matrix representing a similarity graph.
# It is constructed on a sequence of length n=200 with a change in mean 
# in the middle of the sequence (tau = 100).

r1 = gseg1(n,E1, statistics="all")  
# output results based on all four statistics
# the scan statistics can be found in r1$scanZ
r1_a = gseg1(n,E1, statistics="w")  
# output results based on the weighted edge-count statistic
r1_b = gseg1(n,E1, statistics=c("w","g"))  
# output results based on the weighted edge-count statistic 
# and generalized edge-count statistic


## E2 is an edge matrix representing a similarity graph.
# It is constructed on a sequence of length n=200 with a change in mean 
# away from the middle of the sequence (tau=45).
r2 = gseg1(n,E2,statistic="all")


## E3 is an edge matrix representing a similarity graph.
# It is constructed on a sequence of length n=200 with a change in both mean 
# and variance away from the middle of the sequence (tau = 145).
r3=gseg1(n,E3,statistic="all")


## E4 is an edge matrix representing a similarity graph.
# It is constructed on a sequence of length n=200 with a change in both mean 
# and variance away from the middle of the sequence (tau = 50).
r4=gseg1(n,E4,statistic="all")

# }