| Title:
|
A note on the IPF algorithm when the marginal problem is unsolvable (English) |
| Author:
|
Asci, Claudio |
| Author:
|
Piccioni, Mauro |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
39 |
| Issue:
|
6 |
| Year:
|
2003 |
| Pages:
|
[731]-737 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we analyze the asymptotic behavior of the IPF algorithm for the problem of finding a 2x2x2 contingency table whose pair marginals are all equal to a specified 2x2 table, depending on a parameter. When this parameter lies below a certain threshold the marginal problem has no solution. We show that in this case the IPF has a “period three limit cycle” attracting all positive initial tables, and a bifurcation occur when the parameter crosses the threshold. (English) |
| Keyword:
|
contingency tables |
| Keyword:
|
hierarchical models |
| Keyword:
|
partial maximization algorithms |
| MSC:
|
62H17 |
| MSC:
|
65C60 |
| idZBL:
|
Zbl 1245.62070 |
| idMR:
|
MR2035647 |
| . |
| Date available:
|
2009-09-24T19:58:23Z |
| Last updated:
|
2015-03-24 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135568 |
| . |
| Reference:
|
[1] Csiszár I.: I-divergence geometry of probability distributions and minimization problems.Ann. Probab. 3 (1975), 146–158 MR 0365798, 10.1214/aop/1176996454 |
| Reference:
|
[2] Deming W. E., Stephan F. F.: On a least square adjustment of a sampled frequency table when the expected marginal totals are known.Ann. Math. Statist. 11 (1940), 427–444 MR 0003527, 10.1214/aoms/1177731829 |
| Reference:
|
[3] Haberman S. J.: The analysis of frequency data.The University of Chicago Press, Chicago 1974 Zbl 0325.62017, MR 0408098 |
| Reference:
|
[4] Jensen S. T., Johansen, S., Lauritzen S. L.: Globally convergent algorithms for maximizing a likelihood function.Biometrika 78 (1991), 867–877 Zbl 0752.62031, MR 1147024 |
| Reference:
|
[5] Jiroušek R.: Solution of the marginal problem and decomposable distributions.Kybernetika 27 (1991), 403–412 Zbl 0752.60009, MR 1132602 |
| Reference:
|
[6] Lauritzen S. L.: Graphical Models.Clarendon Press, Oxford 1996 Zbl 1055.62126, MR 1419991 |
| . |
