Binary segmentation and Bonferroni-type bounds
Kybernetika (2011)
- Volume: 47, Issue: 1, page 38-49
- ISSN: 0023-5954
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topČerný, Michal. "Binary segmentation and Bonferroni-type bounds." Kybernetika 47.1 (2011): 38-49. <http://eudml.org/doc/196564>.
@article{Černý2011,
abstract = {We introduce the function $Z(x; \xi , \nu ) := \int _\{-\infty \}^x \varphi (t-\xi )\cdot \Phi (\nu t)\ \text\{d\}t$, where $\varphi $ and $\Phi $ are the pdf and cdf of $N(0,1)$, respectively. We derive two recurrence formulas for the effective computation of its values. We show that with an algorithm for this function, we can efficiently compute the second-order terms of Bonferroni-type inequalities yielding the upper and lower bounds for the distribution of a max-type binary segmentation statistic in the case of small samples (where asymptotic results do not work), and in general for max-type random variables of a certain type. We show three applications of the method – (a) calculation of critical values of the segmentation statistic, (b) evaluation of its efficiency and (c) evaluation of an estimator of a point of change in the mean of time series.},
author = {Černý, Michal},
journal = {Kybernetika},
keywords = {Bonferroni inequality; segmentation statistic; Z-function; Bonferroni inequality; segmentation statistic; Z-function},
language = {eng},
number = {1},
pages = {38-49},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Binary segmentation and Bonferroni-type bounds},
url = {http://eudml.org/doc/196564},
volume = {47},
year = {2011},
}
TY - JOUR
AU - Černý, Michal
TI - Binary segmentation and Bonferroni-type bounds
JO - Kybernetika
PY - 2011
PB - Institute of Information Theory and Automation AS CR
VL - 47
IS - 1
SP - 38
EP - 49
AB - We introduce the function $Z(x; \xi , \nu ) := \int _{-\infty }^x \varphi (t-\xi )\cdot \Phi (\nu t)\ \text{d}t$, where $\varphi $ and $\Phi $ are the pdf and cdf of $N(0,1)$, respectively. We derive two recurrence formulas for the effective computation of its values. We show that with an algorithm for this function, we can efficiently compute the second-order terms of Bonferroni-type inequalities yielding the upper and lower bounds for the distribution of a max-type binary segmentation statistic in the case of small samples (where asymptotic results do not work), and in general for max-type random variables of a certain type. We show three applications of the method – (a) calculation of critical values of the segmentation statistic, (b) evaluation of its efficiency and (c) evaluation of an estimator of a point of change in the mean of time series.
LA - eng
KW - Bonferroni inequality; segmentation statistic; Z-function; Bonferroni inequality; segmentation statistic; Z-function
UR - http://eudml.org/doc/196564
ER -
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