| Title:
|
Binary segmentation and Bonferroni-type bounds (English) |
| Author:
|
Černý, Michal |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
47 |
| Issue:
|
1 |
| Year:
|
2011 |
| Pages:
|
38-49 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Bonferroni inequality |
| Keyword:
|
segmentation statistic |
| Keyword:
|
Z-function |
| MSC:
|
05A20 |
| MSC:
|
62E17 |
| idZBL:
|
Zbl 1209.62014 |
| idMR:
|
MR2807862 |
| . |
| Date available:
|
2011-04-12T13:01:44Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141476 |
| . |
| Reference:
|
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| Reference:
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