cpRho: Test for Change-Point Detection Based on Spearman's Rho

In npcp: Some Nonparametric CUSUM Tests for Change-Point Detection in Possibly Multivariate Observations

Test for Change-Point Detection Based on Spearman's Rho

Description

Nonparametric test for change-point detection particularly sensitive to changes in Spearman's rho in multivariate time series. The observations can be serially independent or dependent (strongly mixing). Approximate p-values 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

cpRho(x, method = c("mult", "asym.var"),
      statistic = c("pairwise", "global"),
      b = NULL, weights = c("parzen", "bartlett"),
      N = 1000, init.seq = NULL, include.replicates = FALSE)

Arguments

x	a data matrix whose rows are multivariate continuous observations.
method	a string specifying the method for computing the approximate p-value for the test statistic; can be either "mult" (the multiplier approach 'tilde' in the first reference) or "asym.var" (the approach based on the estimation of the asymptotic null distribution of the test statistic described in the first reference). The 'mult' approach appears to lead to better behaved tests.
statistic	a string specifying the test statistic; can be either "pairwise" (the statistic S_{n,3} in the first reference) or "global" (the statistic S_{n,1} in the first reference).
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 NULL, b will be estimated from x using the procedure described in the first reference.
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 N * (nrow(x) + 2 * (b - 1)) used to generate dependent multiplier sequences.
include.replicates	a logical specifying whether the object of class htest returned by the function (see below) will include the multiplier replicates, if generated.

Details

When method == "mult", the approximate p-value is computed as

(0.5 +\sum_{i=1}^N\mathbf{1}_{\{S_i\ge S\}})/(N+1),

where S and S_i denote the test statistic and a multiplier replication, respectively. This ensures that the approximate p-value is a number strictly between 0 and 1, which is sometimes necessary for further treatments.

When method == "asym.var", the approximate p-value 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 p-value.
rho	the values of the nrow(x)-1 intermediate change-point statistics; the test statistic is defined as the maximum of those.
b	the value of parameter b.

Note

These tests were derived under the assumption of continuous margins.

References

I. Kojadinovic, J-F. Quessy and T. Rohmer (2016), Testing the constancy of Spearman's rho in multivariate time series, Annals of the Institute of Statistical Mathematics 68:5, pages 929-954, https://arxiv.org/abs/1407.1624.

A. Bücher and I. Kojadinovic (2016), A dependent multiplier bootstrap for the sequential empirical copula process under strong mixing, Bernoulli 22:2, pages 927-968, https://arxiv.org/abs/1306.3930.

See Also

cpTau() for a related test based on Kendall's tau, cpDist() for a related test based on the multivariate empirical d.f., cpCopula() for a related test based on the empirical copula.

Examples

## Not run: 
require(copula)
n <- 100
k <- 50 ## the true change-point
u <- rCopula(k,gumbelCopula(1.5))
v <- rCopula(n-k,gumbelCopula(3))
x <- rbind(u,v)
cp <- cpRho(x, b = 1)
cp
## Estimated change-point
which(cp$rho == max(cp$rho))
## End(Not run)

npcp documentation built on Oct. 18, 2024, 9:06 a.m.