Choosing the best φ -divergence goodness-of-fit statistic in multinomial sampling with linear constraints

Nirian Martin; Leandro Pardo

Kybernetika (2006)

  • Volume: 42, Issue: 6, page 711-722
  • ISSN: 0023-5954

Abstract

top
In this paper we present a simulation study to analyze the behavior of the φ -divergence test statistics in the problem of goodness-of-fit for loglinear models with linear constraints and multinomial sampling. We pay special attention to the Rényi’s and I r -divergence measures.

How to cite

top

Martin, Nirian, and Pardo, Leandro. "Choosing the best $\phi $-divergence goodness-of-fit statistic in multinomial sampling with linear constraints." Kybernetika 42.6 (2006): 711-722. <http://eudml.org/doc/33834>.

@article{Martin2006,
abstract = {In this paper we present a simulation study to analyze the behavior of the $\phi $-divergence test statistics in the problem of goodness-of-fit for loglinear models with linear constraints and multinomial sampling. We pay special attention to the Rényi’s and $I_\{r\}$-divergence measures.},
author = {Martin, Nirian, Pardo, Leandro},
journal = {Kybernetika},
keywords = {multinomial sampling; restricted maximum likelihood estimator; goodness-of-fit; $I_r$-divergence measure; Rényi’s divergence measure; loglinear model; restricted maximum likelihood estimator; -divergence measure; Rényi’s divergence measure},
language = {eng},
number = {6},
pages = {711-722},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Choosing the best $\phi $-divergence goodness-of-fit statistic in multinomial sampling with linear constraints},
url = {http://eudml.org/doc/33834},
volume = {42},
year = {2006},
}

TY - JOUR
AU - Martin, Nirian
AU - Pardo, Leandro
TI - Choosing the best $\phi $-divergence goodness-of-fit statistic in multinomial sampling with linear constraints
JO - Kybernetika
PY - 2006
PB - Institute of Information Theory and Automation AS CR
VL - 42
IS - 6
SP - 711
EP - 722
AB - In this paper we present a simulation study to analyze the behavior of the $\phi $-divergence test statistics in the problem of goodness-of-fit for loglinear models with linear constraints and multinomial sampling. We pay special attention to the Rényi’s and $I_{r}$-divergence measures.
LA - eng
KW - multinomial sampling; restricted maximum likelihood estimator; goodness-of-fit; $I_r$-divergence measure; Rényi’s divergence measure; loglinear model; restricted maximum likelihood estimator; -divergence measure; Rényi’s divergence measure
UR - http://eudml.org/doc/33834
ER -

References

top
  1. Agresti A., Categorical Data Analysis, Wiley, New York 2002 MR1914507
  2. Andersen E. B., The Statistical Analysis of Categorical Data, Springer, New York 1990 Zbl0871.62050
  3. Ali S. M., Silvey S. D., A general class of coefficient of divergence of one distribution from another, J. Roy. Statist. Soc. 28 (1966), 131–142 (1966) MR0196777
  4. Csiszár I., Eine Informationstheoretische Ungleichung und ihre Anwendung auf den Bewis der Ergodizität on Markhoffschen Ketten, Publ. Math. Inst. Hungar. Acad. Sci. 8 (1963), 84–108 (1963) 
  5. Dale J. R., Asymptotic normality of goodness-of-fit statistics for sparse product multinomials, J. Roy. Statist. Soc. Ser. B 41 (1986), 48–59 (1986) Zbl0611.62017MR0848050
  6. Haber M., Brown M. B., Maximum likelihood methods for log-linear models when expected frequencies are subject to linear constraints, J. Amer. Statist. Assoc. 81 (1986), 477–482 (1986) Zbl0604.62058MR0845886
  7. Kullback S., Kullback information, In: Encyclopedia of Statistical Sciences (S. Kotz and N. L. Johnson, eds.), Wiley, New York 1985, Volume 4, pp. 421–425 (1985) MR1044999
  8. Liese F., Vajda I., Convex Statistical Distances, Teubner, Leipzig 1987 Zbl0656.62004MR0926905
  9. Pardo L., Menéndez M. L., 10.1007/s00184-006-0034-2, Metrika 64 (2006), 63–76 Zbl1098.62092MR2242558DOI10.1007/s00184-006-0034-2
  10. Powers D. A., Xie Y., Statistical Methods for Categorical Data Analysis, Academic Press, San Diego 2000 Zbl0967.62101MR1735454
  11. Rényi A., On measures of entropy and information, Proc. Fourth Berkeley Symposium on Mathematical Statistics and Probability 1 (1961), pp. 547–561 (1961) 
  12. Vajda I., Theory of Statistical Inference and Information, Kluwer Academic Publishers, Dordrecht 1989 Zbl0711.62002

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.