| Title:
|
An exploratory canonical analysis approach for multinomial populations based on the $\phi$-divergence measure (English) |
| Author:
|
Pardo, J. A. |
| Author:
|
Pardo, L. |
| Author:
|
Pardo, M. C. |
| Author:
|
Zografos, K. |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
40 |
| Issue:
|
6 |
| Year:
|
2004 |
| Pages:
|
[757]-776 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we consider an exploratory canonical analysis approach for multinomial population based on the $\phi $-divergence measure. We define the restricted minimum $\phi $-divergence estimator, which is seen to be a generalization of the restricted maximum likelihood estimator. This estimator is then used in $\phi $-divergence goodness-of-fit statistics which is the basis of two new families of statistics for solving the problem of selecting the number of significant correlations as well as the appropriateness of the model. (English) |
| Keyword:
|
canonical analysis |
| Keyword:
|
restricted minimum $\phi $-divergence estimator |
| Keyword:
|
minimum $\phi $-divergence statistic |
| Keyword:
|
simulation |
| Keyword:
|
power divergence |
| MSC:
|
62B10 |
| MSC:
|
62F10 |
| MSC:
|
62F30 |
| MSC:
|
62H17 |
| MSC:
|
62H20 |
| idZBL:
|
Zbl 1245.62003 |
| idMR:
|
MR2120396 |
| . |
| Date available:
|
2009-09-24T20:06:06Z |
| Last updated:
|
2015-03-23 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135632 |
| . |
| Reference:
|
[1] Aitchison J., Silvey S. D.: Maximum-likelihood estimation of parameters subject to constraints.Ann. Math. Statist. 29 (1958), 813–828 MR 0094873, 10.1214/aoms/1177706538 |
| Reference:
|
[2] Ali S. M., Silvey S. D.: A general class of coefficients of divergence of one distribution from another.J. Roy. Statist. Soc. Ser. B 26 (1966), 131–142 Zbl 0203.19902, MR 0196777 |
| Reference:
|
[3] Anderson E. B. A.: The Statistical Analysis of Categorical Data.Springer-Verlag, Berlin 1990 |
| Reference:
|
[4] Basu A., Basu S.: .Penalized minimum disparity methods in multinomials models. Statistica Sinica 8 (1998), 841–860 Zbl 1229.81348, MR 1651512 |
| Reference:
|
[5] Basu A., Lindsay B. G.: Minimum disparity estimation for continuous models.Ann. Inst. Statist. Math. 46 (1994), 683–705 Zbl 0821.62018, MR 1325990, 10.1007/BF00773476 |
| Reference:
|
[6] Basu A., Sarkar S.: Minimum disparity estimation in the errors-invariables model.Statist. Probab. Lett. 20 (1994), 69–73 MR 1294806, 10.1016/0167-7152(94)90236-4 |
| Reference:
|
[7] Basu A., Sarkar S.: The trade-off between robustness and efficiency and the effect of model smoothing.J. Statist. Comput. Simul. 50 (1994), 173–185 10.1080/00949659408811609 |
| Reference:
|
[8] Benzecri J. P.: L’Analyse des Données.Tome 2: L’Analyse des Correspondances. Dunod, Paris 1973 Zbl 0632.62002 |
| Reference:
|
[9] Birch M. W.: A new proof of the Pearson–Fisher theorem.Ann. Math. Statist. 35 (1964), 817–824 Zbl 0259.62017, MR 0169324, 10.1214/aoms/1177703581 |
| Reference:
|
[10] Cressie N. A. C., Pardo L.: Minimum $\phi $-divergence estimator and hierarchical testing in loglinear models.Statistica Sinica 10 (2000), 867–884 Zbl 0969.62047, MR 1787783 |
| Reference:
|
[11] Cressie N. A. C., Pardo L.: Model checking in loglinear models using $\phi $-divergences and MLEs.J. Statist. Plann. Inference 103 (2002), 437–453 Zbl 0988.62041, MR 1897005, 10.1016/S0378-3758(01)00236-1 |
| Reference:
|
[12] Cressie N. A. C., Read T. R. C.: Multinomial goodness-of-fit tests.J. Roy. Statist. Soc. Ser. B 46 (1984), 440–464 Zbl 0571.62017, MR 0790631 |
| Reference:
|
[13] Crichton N. J., Hinde J. P.: Correspondence analysis as a screening method for indicants for clinical diagnosis.Statistics in Medicine 8 (1989), 1351–1362 10.1002/sim.4780081107 |
| Reference:
|
[14] Csiszár I.: Eine Informationstheoretische Ungleichung und ihre Anwendung auf den Beweis der Ergodizität on Markhoffschen Ketten.Publ. Math. Inst. Hungar. Acad. Sci. Ser. A 8 (1963), 85–108 MR 0164374 |
| Reference:
|
[15] Dahdouh B., Durantan J. F., Lecoq M.: Analyse des donnée sur l’ecologie des acridients d’Afrique de lóuest.Cahiers de l’ Analyse des Données 3 (1978), 459–482 |
| Reference:
|
[16] Fasham M. J. R.: A comparison of nonmetric multidimensional scaling, principal components averaging for the ordination of simulated coenocicles, and coenoplanes.Ecology 58 (1977), 551–561 10.2307/1939004 |
| Reference:
|
[17] Gilula Z., Haberman J.: Canonical Analysis of Contingency Tables by Maximum Likelihood.J. Amer. Statist. Assoc. 81 (1986), 395, 780–788 Zbl 0623.62047, MR 0860512, 10.1080/01621459.1986.10478335 |
| Reference:
|
[18] Greenacre M. J.: Theory and Applications of Correspondence Analysis.Academic Press, New York 1984 Zbl 0555.62005, MR 0767260 |
| Reference:
|
[19] Greenacre M.: Correspondence analysis in medical research.Statist. Meth. Medic. Res. 1 (1992), 97–117 10.1177/096228029200100106 |
| Reference:
|
[20] Greenacre M. J.: Correspondence Analysis in Practice.Academic Press, London 1993 Zbl 1198.62061 |
| Reference:
|
[21] Greenacre M. J.: Correspondence Analysis of the Spanish National Health Survey.Department of Economics and Business, Universitat Pompeu Fabra, Barcelona 2002 |
| Reference:
|
[22] Lancaster H. O.: The Chi-squared Distribution.Wiley, New York 1969 Zbl 0193.17802, MR 0253452 |
| Reference:
|
[23] Lebart L., Morineau, A., Warwick K.: Multivariate Descriptive Statistical Analysis.Wiley, New York 1984 Zbl 0658.62069, MR 0744990 |
| Reference:
|
[24] Lindsay B. G.: Efficiency versus robustness.The case for minimum Hellinger distance and other methods. Ann. Statist. 22 (1994), 1081–1114 Zbl 0807.62030, MR 1292557, 10.1214/aos/1176325512 |
| Reference:
|
[25] Matthews G. B., Crowther N. A. S.: A maximum likelihood estimation procedure when modelling categorical data in terms of cross-product ratios.South African Statist. J. 31 (1997), 161–184 Zbl 0901.62075, MR 1614469 |
| Reference:
|
[26] Matthews G. B., Crowther N. A. S.: A maximum likelihood estimation procedures when modeling in terms of constraints.South African Statist. J. 29 (1995), 29–50 MR 1369086 |
| Reference:
|
[27] Morales D., Pardo, L., Vajda I.: Asymptotic divergence of estimates of discrete distributions.J. Statist. Plann. Inference 48 (1995), 347–369 Zbl 0839.62004, MR 1368984, 10.1016/0378-3758(95)00013-Y |
| Reference:
|
[28] Parr W. C.: Minimum distance estimation: a bibliography.Comm. Statist. Theory Methods 10 (1981), 1205–1224 Zbl 0458.62035, MR 0623527, 10.1080/03610928108828104 |
| Reference:
|
[29] Pardo J. A., Pardo, L., Zografos K.: Minimum $\phi $-divergence estimators with constraints in multinomial populations.J. Statist. Plann. Inference 104 (2002), 221–237 Zbl 0988.62014, MR 1900527, 10.1016/S0378-3758(01)00113-6 |
| Reference:
|
[30] Read T. R. C., Cressie N. A. C.: Goodness-of-fit Statistics for Discrete Multivariate Data.Springer, New York 1988 Zbl 0663.62065, MR 0955054 |
| Reference:
|
[31] Srole L., Langner T. S., Michael S. T., Opler M. K., Reannie T. A. C.: Mental Health in the Metropolis: The Midtown Manhattan Study.McGraw-Hill, New York 1962 |
| Reference:
|
[32] Wolfowitz J.: Estimation by minimum distance method.Ann. Inst. Statist. Math. 5 (1953), 9–23 MR 0058931, 10.1007/BF02949797 |
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