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This function finds a break point in the sequence where the underlying distribution changes. It provides four graph-based test statistics.
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)The number of observations in the sequence.
The edge matrix (a "number of edges" by 2 matrix) for the similarity graph. Each row contains the node indices of an edge.
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.
The starting index to be considered as a candidate for the change-point.
The ending index to be considered as a candidate for the change-point.
If it is TRUE, the function outputs p-value approximation based on asymptotic properties.
This argument is useful only when pval.appr=TRUE. If skew.corr is TRUE, the p-value approximation would incorporate skewness correction.
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.
This argument is useful only when pval.perm=TRUE. The default value for B is 100.
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.
An estimate of the location of the change-point.
The test statistic (maximum of the scan statistics).
A vector of the original scan statistics (standardized counts) if statistic specified is "all" or "o".
A vector of the weighted scan statistics (standardized counts) if statistic specified is "all" or "w".
A vector of the generalized scan statistics (standardized counts) if statistic specified is "all" or "g".
A vector of the max-type scan statistics (standardized counts) if statistic specified is "all" or "m".
A vector of raw counts of the original scan statistic. This output only exists if the statistic specified is "all" or "o".
A vector of raw counts of the weighted scan statistic. This output only exists if statistic specified is "all" or "w".
The approximated p-value based on asymptotic theory for each type of statistic specified.
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).
A B by 2 matrix with the first column being critical values corresponding to the p-values in the second column.
A sorted vector recording the test statistics in the B permutaitons.
A B by n matrix with each row being the scan statistics from each permutaiton run.
# 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")
# }
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