Some tests for changepoint detection based on Ustatistics
Description
Nonparametric tests for changepoint detection particularly sensitive to changes in certain quantities that can be estimated using onesample Ustatistics of order two. Thus far, the quantities under consideration are the variance, Gini's mean difference and Kendall's tau (a generic mecanism for defining the Ustatistic will be implemented in future releases). The observations can be serially independent or dependent (strongly mixing). Approximate pvalues for the test statistic are obtained by means of a multiplier approach or by estimating the asymptotic null distribution. Details can be found in first reference.
Usage
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Arguments
x 
a data matrix whose rows are continuous observations. 
statistic 
a string specifying the statistic of interest;
can be either 
method 
a string specifying the method for computing the
approximate pvalue for 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 default
value is 1, which will create i.i.d. multiplier
sequences suitable for serially independent observations. If set to

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. 
N 
number of multiplier replications. 
init.seq 
a sequence of independent standard normal variates of
length 
Details
When method
is either "seq"
or "nonseq"
,
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.
When method == "asym.var"
, the approximate pvalue is computed
from the estimated asymptotic null distribution, which involves the
Kolmogorov distribution. The latter is dealt with reusing code from
the ks.test()
function; credit to RCore.
Value
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. 
u 
the values of the 
b 
the value of parameter 
Note
A generic mecanism for defining the Ustatistic will be implemented in future releases.
References
A. Bücher and I. Kojadinovic (2014), Dependent multiplier bootstraps for nondegenerate Ustatistics under mixing conditions with applications, http://arxiv.org/abs/1412.5875.
A. Bücher and I. Kojadinovic (2014), A dependent multiplier bootstrap for the sequential empirical copula process under strong mixing, Bernoulli, in press, http://arxiv.org/abs/1306.3930.
See Also
cpTestFn()
for a related test based on the multivariate
empirical c.d.f., cpTestCn()
for a related test based on
the empirical copula, cpTestRho()
for a related test based on
Spearman's rho.
Examples
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