Geodesic
Existence, Consistency and computer simulation for selected variants of minimum distance estimators
Kybernetika, Tome 54 (2018) no. 2, pp. 336-350 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

The paper deals with sufficient conditions for the existence of general approximate minimum distance estimator (AMDE) of a probability density function $f_0$ on the real line. It shows that the AMDE always exists when the bounded $\phi$-divergence, Kolmogorov, Lévy, Cramér, or discrepancy distance is used. Consequently, $n^{-1/2}$ consistency rate in any bounded $\phi$-divergence is established for Kolmogorov, Lévy, and discrepancy estimators under the condition that the degree of variations of the corresponding family of densities is finite. A simulation experiment empirically studies the performance of the approximate minimum Kolmogorov estimator (AMKE) and some histogram-based variants of approximate minimum divergence estimators, like power type and Le Cam, under six distributions (Uniform, Normal, Logistic, Laplace, Cauchy, Weibull). A comparison with the standard estimators (moment/maximum likelihood/median) is provided for sample sizes $n=10,20,50,120,250$. The simulation analyzes the behaviour of estimators through different families of distributions. It is shown that the performance of AMKE differs from the other estimators with respect to family type and that the AMKE estimators cope more easily with the Cauchy distribution than standard or divergence based estimators, especially for small sample sizes.
The paper deals with sufficient conditions for the existence of general approximate minimum distance estimator (AMDE) of a probability density function $f_0$ on the real line. It shows that the AMDE always exists when the bounded $\phi$-divergence, Kolmogorov, Lévy, Cramér, or discrepancy distance is used. Consequently, $n^{-1/2}$ consistency rate in any bounded $\phi$-divergence is established for Kolmogorov, Lévy, and discrepancy estimators under the condition that the degree of variations of the corresponding family of densities is finite. A simulation experiment empirically studies the performance of the approximate minimum Kolmogorov estimator (AMKE) and some histogram-based variants of approximate minimum divergence estimators, like power type and Le Cam, under six distributions (Uniform, Normal, Logistic, Laplace, Cauchy, Weibull). A comparison with the standard estimators (moment/maximum likelihood/median) is provided for sample sizes $n=10,20,50,120,250$. The simulation analyzes the behaviour of estimators through different families of distributions. It is shown that the performance of AMKE differs from the other estimators with respect to family type and that the AMKE estimators cope more easily with the Cauchy distribution than standard or divergence based estimators, especially for small sample sizes.
DOI : 10.14736/kyb-2018-2-0336
Classification : 62B05, 62H30
Keywords: Kolmogorov distance; $\phi $-divergence; minimum distance estimator; consistency rate; computer simulation 
@article{10_14736_kyb_2018_2_0336,
     author = {K\r{u}s, V\'aclav and Morales, Domingo and Hrab\'akov\'a, Jitka and Fr\'ydlov\'a, Iva},
     title = {Existence, {Consistency} and computer simulation for selected variants of minimum distance estimators},
     journal = {Kybernetika},
     pages = {336--350},
     year = {2018},
     volume = {54},
     number = {2},
     doi = {10.14736/kyb-2018-2-0336},
     mrnumber = {3807719},
     zbl = {06890424},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2018-2-0336/}
}
TY  - JOUR
AU  - Kůs, Václav
AU  - Morales, Domingo
AU  - Hrabáková, Jitka
AU  - Frýdlová, Iva
TI  - Existence, Consistency and computer simulation for selected variants of minimum distance estimators
JO  - Kybernetika
PY  - 2018
SP  - 336
EP  - 350
VL  - 54
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.14736/kyb-2018-2-0336/
DO  - 10.14736/kyb-2018-2-0336
LA  - en
ID  - 10_14736_kyb_2018_2_0336
ER  - 
%0 Journal Article
%A Kůs, Václav
%A Morales, Domingo
%A Hrabáková, Jitka
%A Frýdlová, Iva
%T Existence, Consistency and computer simulation for selected variants of minimum distance estimators
%J Kybernetika
%D 2018
%P 336-350
%V 54
%N 2
%U http://geodesic.mathdoc.fr/articles/10.14736/kyb-2018-2-0336/
%R 10.14736/kyb-2018-2-0336
%G en
%F 10_14736_kyb_2018_2_0336
Kůs, Václav; Morales, Domingo; Hrabáková, Jitka; Frýdlová, Iva. Existence, Consistency and computer simulation for selected variants of minimum distance estimators. Kybernetika, Tome 54 (2018) no. 2, pp. 336-350. doi: 10.14736/kyb-2018-2-0336

Cité par Sources :