e.divisive {ecp}

ENERGY DIVISIVE

Description

A divisive hierarchical estimation algorithm for multiple change point analysis.

Usage

e.divisive(X, sig.lvl=.05, R=199, k=NULL, min.size=30, alpha=1)

Arguments

X

A T x d matrix containing the length T time series with d-dimensional observations.

sig.lvl

The level at which to sequentially test if a proposed change point is statistically significant.

R

The maximum number of random permutations to use in each iteration of the permutation test. The permutation test p-value is calculated using the method outlined in Gandy (2009).

k

Number of change point locations to estimate, suppressing permutation based testing. If k=NULL then only the statistically significant estimated change points are returned.

min.size

Minimum number of observations between change points.

alpha

The moment index used for determining the distance between and within segments.

Details

Segments are found through the use of a binary bisection method and a permutation test. The computational complexity of this method is O(kT^2), where k is the number of estimated change points, and T is the number of observations.

Value

The returned value is a list with the following components.

k.hat

The number of clusters within the data created by the change points.

order.found

The order in which the change points were estimated.

estimates

Locations of the statistically significant change points.

considered.last

Location of the last change point, that was not found to be statistically significant at the given significance level.

permutations

The number of permutations performed by each of the sequential permutation test.

cluster

The estimated cluster membership vector.

p.values

Approximate p-values estimated from each permutation test.

Author(s)

Nicholas A. James

References

Matteson D.S., James N.A. (2013). A Nonparametric Approach for Multiple Change Point Analysis of Multivariate Data.

Nicholas A. James, David S. Matteson (2014). "ecp: An R Package for Nonparametric Multiple Change Point Analysis of Multivariate Data.", "Journal of Statistical Software, 62(7), 1-25", URL "http://www.jstatsoft.org/v62/i07/"

See Also

e.agglo

Gandy, A. (2009) "Sequential implementation of Monte Carlo tests with uniformly bounded resampling risk." Journal of the American Statistical Association.

Rizzo M.L., Szekely G.L (2005). Hierarchical clustering via joint between-within distances: Extending ward's minimum variance method. Journal of Classification.

Rizzo M.L., Szekely G.L. (2010). Disco analysis: A nonparametric extension of analysis of variance. The Annals of Applied Statistics.

Examples

set.seed(100)
x1 = matrix(c(rnorm(100),rnorm(100,3),rnorm(100,0,2)))
y1 = e.divisive(X=x1,sig.lvl=0.05,R=199,k=NULL,min.size=30,alpha=1)
x2 = rbind(MASS::mvrnorm(100,c(0,0),diag(2)),
	MASS::mvrnorm(100,c(2,2),diag(2)))
y2 = e.divisive(X=x2,sig.lvl=0.05,R=499,k=NULL,min.size=30,alpha=1)