e.divisive {ecp} | R Documentation |

A divisive hierarchical estimation algorithm for multiple change point analysis.

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

`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. |

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.

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. |

Nicholas A. James

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/"

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.

```
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)
```

[Package *ecp* version 3.1.3 Index]