model.ic {breakfast}

Estimating change-points or change-point-type features in the mean of a noisy data sequence via the strengthened Schwarz information criterion

Description

This function estimates the number and locations of change-points or change-point-type features in the mean of a noisy data sequence via the sSIC (strengthened Schwarz information criterion) method.

Usage

model.ic(cptpath.object, alpha = 1.01, q.max = NULL)

Arguments

cptpath.object

A solution-path object, returned by a sol.[name] routine. Note that the field cptpath.object$x contains the input data sequence.

alpha

The parameter associated with the sSIC. The default value is 1.01. Note that the SIC is recovered when alpha = 1.

q.max

The maximum number of features allowed. If nothing or NULL is provided, the default value of min(100, n/log(n)) (rounded to an integer) will be used.

Details

The model selection method for algorithms that produce nested solution path is described in "Wild binary segmentation for multiple change-point detection", P. Fryzlewicz (2014), The Annals of Statitics, 42: 2243–2281. The corresponding description for those that produce non-nested solution set can be found in "Narrowest-over-threshold detection of multiple change points and change-point-like features", R. Baranowski, Y. Chen and P. Fryzlewicz (2019), Journal of Royal Statistical Society: Series B, 81(3), 649–672.

Value

An S3 object of class cptmodel, which contains the following fields:

solution.path

The solution path method used to obtain cptpath.object

type

The model type used, inherited from the given cptpath.object

model.selection

The model selection method used to return the final change-point or change-point-type feature estimators object, here its value is "ic"

no.of.cpt

The number of estimated features in the mean of the vector cptpath.object$x based on the given type of the model

cpts

The locations of estimated features in the mean of the vector cptpath.object$x. These are the end-points of the corresponding constant-mean or constant-slope intervals

est

An estimate of the mean of the vector cptpath.object$x; for piecewise-constant signals, the values are the sample means of the data (replicated a suitable number of times) between each pair of consecutive detected change-points; for piecewise-linear but discontinuous signals, the values are based on the estimated linear trend between each pair of consecutive detected change of slopes; for piecewise-linear and continuous signals, it is similar to the previous case but with the continuity constraint enforced, which envolves solving a global least squares problem.

References

P. Fryzlewicz (2014). Wild binary segmentation for multiple change-point detection. The Annals of Statistics, 42(6), 2243–2281.

R. Baranowski, Y. Chen & P. Fryzlewicz (2019). Narrowest-over-threshold detection of multiple change points and change-point-like features. Journal of the Royal Statistical Society: Series B, 81(3), 649–672.

See Also

sol.idetect, sol.not, sol.tguh, sol.wbs, sol.wbs2, breakfast

Examples

x <- c(rep(0, 100), rep(1, 100), rep(0, 100)) + rnorm(300)
model.ic(sol.wbs(x))
model.ic(sol.not(x))