| Title:
|
Modified power divergence estimators in normal models – simulation and comparative study (English) |
| Author:
|
Frýdlová, Iva |
| Author:
|
Vajda, Igor |
| Author:
|
Kůs, Václav |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
48 |
| Issue:
|
4 |
| Year:
|
2012 |
| Pages:
|
795-808 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Point estimators based on minimization of information-theoretic divergences between empirical and hypothetical distribution induce a problem when working with continuous families which are measure-theoretically orthogonal with the family of empirical distributions. In this case, the $\phi$-divergence is always equal to its upper bound, and the minimum $\phi$-divergence estimates are trivial. Broniatowski and Vajda [3] proposed several modifications of the minimum divergence rule to provide a solution to the above mentioned problem. We examine these new estimation methods with respect to consistency, robustness and efficiency through an extended simulation study. We focus on the well-known family of power divergences parametrized by $\alpha \in \mathbb{R}$ in the Gaussian model, and we perform a comparative computer simulation for several randomly selected contaminated and uncontaminated data sets, different sample sizes and different $\phi$-divergence parameters. (English) |
| Keyword:
|
minimum $\phi $-divergence estimation |
| Keyword:
|
subdivergence |
| Keyword:
|
superdivergence |
| Keyword:
|
PC simulation |
| Keyword:
|
relative efficiency |
| Keyword:
|
robustness |
| MSC:
|
62B05 |
| MSC:
|
62H30 |
| idMR:
|
MR3013399 |
| . |
| Date available:
|
2012-11-10T22:09:24Z |
| Last updated:
|
2013-09-24 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143060 |
| . |
| Reference:
|
[1] M. Broniatowski, A. Keziou: Minimization of $\phi $-divergences on sets of signed measures..Studia Sci. Math. Hungar. 43 (2006), 403-442. Zbl 1121.28004, MR 2273419 |
| Reference:
|
[2] M. Broniatowski, A. Keziou: Parametric estimation and tests through divergences and the duality technique..J. Multivariate Anal. 100 (2009), 16-36. Zbl 1151.62023, MR 2460474, 10.1016/j.jmva.2008.03.011 |
| Reference:
|
[3] M. Broniatowski, I. Vajda: Several Applications of Divergence Criteria in Continuous Families..Research Report No. 2257. Institute of Information Theory and Automation, Prague 2009. |
| Reference:
|
[4] I. Frýdlová: Minimum Kolmogorov Distance Estimators..Diploma Thesis. Czech Technical University, Prague 2004. |
| Reference:
|
[5] I. Frýdlová: Modified Power Divergence Estimators and Their Performances in Normal Models..In: Proc. FernStat2010, Faculty of Social and Economic Studies UJEP, Ústí n. L. 2010, 28-33. |
| Reference:
|
[6] F. Liese, I. Vajda: On divergences and informations in statistics and information theory..IEEE Trans. Inform. Theory 52 (2006), 4394-4412. MR 2300826, 10.1109/TIT.2006.881731 |
| Reference:
|
[7] A. Toma, S. Leoni-Aubin: Robust tests based on dual divergence estimators and saddlepoint approximations..J. Multivariate Anal. 101 (2010), 1143-1155. Zbl 1185.62042, MR 2595297, 10.1016/j.jmva.2009.11.001 |
| Reference:
|
[8] A. Toma, M. Broniatowski: Dual divergence estimators and tests: Robustness results..J. Multivariate Analysis 102 (2011), 20-36. Zbl 1206.62034, MR 2729417, 10.1016/j.jmva.2010.07.010 |
| Reference:
|
[9] I. Vajda: Theory of Statistical Inference and Information..Kluwer, Boston 1989. Zbl 0711.62002 |
| . |
