## The Annals of Statistics

### Tail-greedy bottom-up data decompositions and fast multiple change-point detection

Piotr Fryzlewicz

#### Abstract

This article proposes a “tail-greedy”, bottom-up transform for one-dimensional data, which results in a nonlinear but conditionally orthonormal, multiscale decomposition of the data with respect to an adaptively chosen unbalanced Haar wavelet basis. The “tail-greediness” of the decomposition algorithm, whereby multiple greedy steps are taken in a single pass through the data, both enables fast computation and makes the algorithm applicable in the problem of consistent estimation of the number and locations of multiple change-points in data. The resulting agglomerative change-point detection method avoids the disadvantages of the classical divisive binary segmentation, and offers very good practical performance. It is implemented in the R package breakfast, available from CRAN.

#### Article information

Source
Ann. Statist., Volume 46, Number 6B (2018), 3390-3421.

Dates
Revised: September 2017
First available in Project Euclid: 11 September 2018

https://projecteuclid.org/euclid.aos/1536631278

Digital Object Identifier
doi:10.1214/17-AOS1662

Mathematical Reviews number (MathSciNet)
MR3852656

Zentralblatt MATH identifier
06965692

Subjects
Primary: 62G05: Estimation

#### Citation

Fryzlewicz, Piotr. Tail-greedy bottom-up data decompositions and fast multiple change-point detection. Ann. Statist. 46 (2018), no. 6B, 3390--3421. doi:10.1214/17-AOS1662. https://projecteuclid.org/euclid.aos/1536631278

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#### Supplemental materials

• Supplement to “Tail-greedy bottom-up data decompositions and fast multiple change-point detection”. Extension of the TGUH methodology to dependent non-Gaussian data; refinements to post-processing; study of the accuracy of TGUH in estimating change-point locations; additional figure for the analysis of Section 4.3.