# Minimum disparity estimators for discrete and continuous models

María Luisa Menéndez; Domingo Morales; Leandro Pardo; Igor Vajda

Applications of Mathematics (2001)

- Volume: 46, Issue: 6, page 439-466
- ISSN: 0862-7940

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topMenéndez, María Luisa, et al. "Minimum disparity estimators for discrete and continuous models." Applications of Mathematics 46.6 (2001): 439-466. <http://eudml.org/doc/33096>.

@article{Menéndez2001,

abstract = {Disparities of discrete distributions are introduced as a natural and useful extension of the information-theoretic divergences. The minimum disparity point estimators are studied in regular discrete models with i.i.d. observations and their asymptotic efficiency of the first order, in the sense of Rao, is proved. These estimators are applied to continuous models with i.i.d. observations when the observation space is quantized by fixed points, or at random, by the sample quantiles of fixed orders. It is shown that the random quantization leads to estimators which are robust in the sense of Lindsay [9], and which can achieve the efficiency in the underlying continuous models provided these are regular enough.},

author = {Menéndez, María Luisa, Morales, Domingo, Pardo, Leandro, Vajda, Igor},

journal = {Applications of Mathematics},

keywords = {divergence; disparity; minimum disparity estimators; robustness; asymptotic efficiency; divergence; disparity; minimum disparity estimators; robustness; asymptotic efficiency},

language = {eng},

number = {6},

pages = {439-466},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Minimum disparity estimators for discrete and continuous models},

url = {http://eudml.org/doc/33096},

volume = {46},

year = {2001},

}

TY - JOUR

AU - Menéndez, María Luisa

AU - Morales, Domingo

AU - Pardo, Leandro

AU - Vajda, Igor

TI - Minimum disparity estimators for discrete and continuous models

JO - Applications of Mathematics

PY - 2001

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 46

IS - 6

SP - 439

EP - 466

AB - Disparities of discrete distributions are introduced as a natural and useful extension of the information-theoretic divergences. The minimum disparity point estimators are studied in regular discrete models with i.i.d. observations and their asymptotic efficiency of the first order, in the sense of Rao, is proved. These estimators are applied to continuous models with i.i.d. observations when the observation space is quantized by fixed points, or at random, by the sample quantiles of fixed orders. It is shown that the random quantization leads to estimators which are robust in the sense of Lindsay [9], and which can achieve the efficiency in the underlying continuous models provided these are regular enough.

LA - eng

KW - divergence; disparity; minimum disparity estimators; robustness; asymptotic efficiency; divergence; disparity; minimum disparity estimators; robustness; asymptotic efficiency

UR - http://eudml.org/doc/33096

ER -

## References

top- 10.1016/0167-7152(94)90236-4, Statist. Probab. Lett. 20 (1994), 69–73. (1994) MR1294806DOI10.1016/0167-7152(94)90236-4
- 10.1080/00949659408811609, J. Statist. Comput. Simulation 50 (1994), 173–185. (1994) DOI10.1080/00949659408811609
- 10.1214/aoms/1177703581, Ann. Math. Statist. 35 (1964), 817–824. (1964) Zbl0259.62017MR0169324DOI10.1214/aoms/1177703581
- Goodness-of-fit using sample quantiles, J. Roy. Statist. Soc. Ser. B 35 (1973), 277–284. (1973) MR0336896
- Mathematical Methods of Statistics, Princeton University Press, Princeton, 1946. (1946) MR0016588
- Multinomial goodness-of-fit tests, J. Roy. Statist. Soc. Ser. B 46 (1984), 440–464. (1984) MR0790631
- Statistical Methods for Research Workers (8th edition), London, 1941. (1941)
- Convex Statistical Distances, Teubner, Leipzig, 1987. (1987) MR0926905
- 10.1214/aos/1176325512, Ann. Statist. 22 (1994), 1081–1114. (1994) MR1292557DOI10.1214/aos/1176325512
- 10.1080/03610929808832117, Comm. Statist. Theory Methods 27 (1998), 609–633. (1998) MR1619038DOI10.1080/03610929808832117
- 10.1023/A:1012466605316, Ann. Inst. Statist. Math. 53 (2001), 277–288. (2001) MR1841136DOI10.1023/A:1012466605316
- 10.1016/0378-3758(95)00013-Y, J. Statist. Plann. Inference 48 (1995), 347–369. (1995) MR1368984DOI10.1016/0378-3758(95)00013-Y
- Contribution to the theory of the ${\chi}^{2}$ test, In: Proc. Berkeley Symp. Math. Statist. Probab., Berkeley, CA, Berkeley University Press, Berkeley, 1949, pp. 239–273. (1949) MR0028003
- 10.1080/03610919508813265, Comm. Statist. Simulation Comput. 24 (1995), 653–673. (1995) DOI10.1080/03610919508813265
- Asymptotic efficiency and limiting information, In: Proc. 4th Berkeley Symp. Math. Stat. Probab., Berkeley, CA, Berkeley University Press, Berkeley, 1961, pp. 531–545. (1961) Zbl0156.39802MR0133192
- Linear Statistical Inference and its Applications (2nd edition), Wiley, New York, 1973. (1973) MR0346957
- Goodness-of-fit Statistics for Discrete Multivariate Data, Springer-Verlag, New York, 1988. (1988) MR0955054
- On minimum discrepancy estimators, Sankhyä Ser. A 34 (1972), 133–144. (1972) Zbl0266.62021MR0331606
- ${\chi}^{2}$-divergence and generalized Fisher information, In: Transactions of the Sixth Prague Conference on Information Theory, Statistical Decision Functions and Random Processes, Academia, Prague, 1973, pp. 223–234. (1973) Zbl0297.62003MR0356302
- Theory of Statistical Inference and Information, Kluwer Academic Publishers, Boston, 1989. (1989) Zbl0711.62002
- Mathematische Statistik, Springer-Verlag, Berlin, 1957. (1957)
- On the criterion that a given system of deviations from the probable in the case of correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling, Philosophical Magazine 50 (1990), 157–172. (1990)
- Eine Informationstheoretische Ungleichung und ihre Anwendung auf den Beweis der Ergodizität von Markoffschen Ketten, Publications of the Mathematical Institute of the Hungarian Academy of Sciences, Series A 8 (1963), 85–108. (1963) MR0164374
- A general class of coefficients of divergence of one distribution from another, J. Roy. Statist. Soc. Ser. B 28 (1966), 131–140. (1966) MR0196777
- On measures of entropy and information, In: Proceedings of the 4th Berkeley Symposium on Probability Theory and Mathematical Statistics, Vol. 1, University of California Press, Berkeley, 1961, pp. 531–546. (1961) MR0132570
- Inequalities: Theory of Majorization and its Applications, Academic Press, New York, 1979. (1979) MR0552278

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