Existence, Consistency and Computer Simulation for Selected Variants of Minimum Distance Estimators
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F18%3A00316345" target="_blank" >RIV/68407700:21240/18:00316345 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21340/18:00316345
Result on the web
<a href="http://dx.doi.org/10.14736/kyb-2018-2-0336" target="_blank" >http://dx.doi.org/10.14736/kyb-2018-2-0336</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.14736/kyb-2018-2-0336" target="_blank" >10.14736/kyb-2018-2-0336</a>
Alternative languages
Result language
angličtina
Original language name
Existence, Consistency and Computer Simulation for Selected Variants of Minimum Distance Estimators
Original language description
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, L'evy, Cram'er, or discrepancy distance is used. Consequently, $n^{-1/2}$ consistency rate in any bounded $phi$-divergence is established for Kolmogorov, L'evy, 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.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10103 - Statistics and probability
Result continuities
Project
—
Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Kybernetika
ISSN
0023-5954
e-ISSN
—
Volume of the periodical
54
Issue of the periodical within the volume
2
Country of publishing house
CZ - CZECH REPUBLIC
Number of pages
15
Pages from-to
336-350
UT code for WoS article
000435168400008
EID of the result in the Scopus database
2-s2.0-85047380840