cpDist  R Documentation 
Nonparametric test for changepoint detection based on the (multivariate) empirical distribution function. The observations can be continuous univariate or multivariate, and serially independent or dependent (strongly mixing). Approximate pvalues for the test statistics are obtained by means of a multiplier approach. The first reference treats the serially independent case while details about the serially dependent case can be found in second and third references.
cpDist(x, statistic = c("cvmmax", "cvmmean", "ksmax", "ksmean"), method = c("nonseq", "seq"), b = NULL, gamma = 0, delta = 1e4, weights = c("parzen", "bartlett"), m = 5, L.method=c("max","median","mean","min"), N = 1000, init.seq = NULL, include.replicates = FALSE)
x 
a data matrix whose rows are continuous observations. 
statistic 
a string specifying the statistic whose value and
pvalue will be displayed; can be either 
method 
a string specifying the simulation method for
generating multiplier replicates of the test statistic;
can be either 
b 
strictly positive integer specifying the value of the
bandwidth parameter determining the serial dependence when
generating dependent multiplier sequences using the 'moving average
approach'; see Section 5 of the second reference. The
value 1 will create i.i.d. multiplier
sequences suitable for serially independent observations. If set to

gamma 
parameter between 0 and 0.5 appearing in the definition of the weight function used in the detector function. 
delta 
parameter between 0 and 1 appearing in the definition of the weight function used in the detector function. 
weights 
a string specifying the kernel for creating the weights used in the generation of dependent multiplier sequences within the 'moving average approach'; see Section 5 of the second reference. 
m 
a strictly positive integer specifying the number of points of the
uniform grid on (0,1)^d (where d is

L.method 
a string specifying how the parameter L involved in the estimation of the bandwidth parameter is computed; see Section 5 of the second reference. 
N 
number of multiplier replications. 
init.seq 
a sequence of independent standard normal variates of
length 
include.replicates 
a logical specifying whether the
object of 
The approximate pvalue is computed as
(0.5 + sum(S[i] >= S, i=1, .., N)) / (N+1),
where S and S[i] denote the test statistic and a multiplier replication, respectively. This ensures that the approximate pvalue is a number strictly between 0 and 1, which is sometimes necessary for further treatments.
An object of class
htest
which is a list,
some of the components of which are
statistic 
value of the test statistic. 
p.value 
corresponding approximate pvalue. 
cvm 
the values of the 
ks 
the values of the 
all.statistics 
the values of all four test statistics. 
all.p.values 
the corresponding pvalues. 
b 
the value of parameter 
Note that when the observations are continuous univariate and serially independent, independent realizations of the tests statistics under the null hypothesis of no change in the distribution can be obtained by simulation; see Section 4 in the first reference.
M. Holmes, I. Kojadinovic and JF. Quessy (2013), Nonparametric tests for changepoint detection à la Gombay and Horváth, Journal of Multivariate Analysis 115, pages 1632.
A. Bücher and I. Kojadinovic (2016), A dependent multiplier bootstrap for the sequential empirical copula process under strong mixing, Bernoulli 22:2, pages 927968, https://arxiv.org/abs/1306.3930.
A. Bücher, J.D. Fermanian and I. Kojadinovic (2019), Combining cumulative sum changepoint detection tests for assessing the stationarity of univariate time series, Journal of Time Series Analysis 40, pages 124150, https://arxiv.org/abs/1709.02673.
cpCopula()
for a related test based on the empirical
copula, cpRho()
for a related test based on
Spearman's rho, cpTau()
for a related test based on
Kendall's tau, bOptEmpProc()
for the function used to
estimate b
from x
if b = NULL
,
seqClosedEndCpDist
for the corresponding sequential test.
## A univariate example n < 100 k < 50 ## the true changepoint y < rnorm(k) z < rexp(nk) x < matrix(c(y,z)) cp < cpDist(x, b = 1) cp ## All statistics cp$all.statistics ## Corresponding p.values cp$all.p.values ## Estimated changepoint which(cp$cvm == max(cp$cvm)) which(cp$ks == max(cp$ks)) ## A very artificial trivariate example ## with a break in the first margin n < 100 k < 50 ## the true changepoint y < rnorm(k) z < rnorm(nk, mean = 2) x < cbind(c(y,z),matrix(rnorm(2*n), n, 2)) cp < cpDist(x, b = 1) cp ## All statistics cp$all.statistics ## Corresponding p.values cp$all.p.values ## Estimated changepoint which(cp$cvm == max(cp$cvm)) which(cp$ks == max(cp$ks))
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