gseg2_discrete: Graph-Based Change-Point Detection for Changed Interval for...

In gSeg: Graph-Based Change-Point Detection (g-Segmentation)

Description

This function finds an interval in the sequence where their underlying distribution differs from the rest of the sequence when data has repeated observations. It provides four graph-based test statistics.

Usage

gseg2_discrete(n, E, id, statistics=c("all","o","w","g","m"), l0=0.05*n, l1=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.
id	The index of observations (order of observations).
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.
l0	The minimum length of the interval to be considered as a changed interval.
l1	The maximum length of the interval to be considered as a changed interval.
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_a	An estimate of the two ends of the changed interval for averaging approach.
tauhat_u	An estimate of the two ends of the changed interval for union approach.
Z_a_max	The test statistic (maximum of the scan statistics) for averaging approach.
Z_u_max	The test statistic (maximum of the scan statistics) for union approach.
Zo_a	A matrix of the original scan statistics (standardized counts) for averaging approach if statistic specified is "all" or "o".
Zo_u	A matrix of the original scan statistics (standardized counts) for union approach if statistic specified is "all" or "o".
Zw_a	A matrix of the weighted scan statistics (standardized counts) for averaging approach if statistic specified is "all" or "w".
Zw_u	A matrix of the weighted scan statistics (standardized counts) for union approach if statistic specified is "all" or "w".
S_a	A matrix of the generalized scan statistics (standardized counts) for averaging approach if statistic specified is "all" or "g".
S_u	A matrix of the generalized scan statistics (standardized counts) for union approach if statistic specified is "all" or "g".
M_a	A matrix of the max-type scan statistics (standardized counts) for averaging approach if statistic specified is "all" or "m".
M_u	A matrix of the max-type scan statistics (standardized counts) for union approach if statistic specified is "all" or "m".
Ro_a	A matrix of raw counts of the original scan statistic for averaging approach. This output only exists if the statistic specified is "all" or "o".
Ro_u	A matrix of raw counts of the original scan statistic for union approach. This output only exists if the statistic specified is "all" or "o".
Rw_a	A matrix of raw counts of the weighted scan statistic for averaging approach. This output only exists if statistic specified is "all" or "w".
Rw_a	A matrix of raw counts of the weighted scan statistic for union approach. 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-squared matrix with each row being the vectorized scan statistics from each permutaiton run.

See Also

gSeg, gseg2, nnl, gseg1_discrete

Examples

d = 50
mu = 2
tau = 100
n = 200

set.seed(500)
y1_temp = matrix(rnorm(d*tau),tau)
sam1 = sample(1:tau, replace = TRUE)
y1 = y1_temp[sam1,] 
y2_temp = matrix(rnorm(d*(n-tau),mu/sqrt(d)), n-tau)
sam2 = sample(1:tau, replace = TRUE)
y2 = y2_temp[sam2,] 

y = rbind(y1, y2)

# This data y has repeated observations
y_uni = unique(y)
E = nnl(dist(y_uni), 1)

cha = do.call(paste, as.data.frame(y))    
id = match(cha, unique(cha))

r1 = gseg2_discrete(n, E, id, statistics="all")

gSeg documentation built on Oct. 23, 2020, 5:54 p.m.