Notes on consistency of some minimum distance estimators with simulation results
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F17%3A00304795" target="_blank" >RIV/68407700:21240/17:00304795 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21340/17:00304795
Result on the web
<a href="http://link.springer.com/article/10.1007%2Fs00184-016-0601-0" target="_blank" >http://link.springer.com/article/10.1007%2Fs00184-016-0601-0</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00184-016-0601-0" target="_blank" >10.1007/s00184-016-0601-0</a>
Alternative languages
Result language
angličtina
Original language name
Notes on consistency of some minimum distance estimators with simulation results
Original language description
We focus on the minimum distance density estimators f_n of the true probability density f_0 on the real line. The consistency of the order of n^-1/2 in the (expected) L_1-norm of Kolmogorov estimator (MKE) is known if the degree of variations of the nonparametric family D is finite. Using this result for MKE we prove that minimum Lévy and minimum discrepancy distance estimators are consistent of the order of n^-1/2 in the (expected) L_1-norm under the same assumptions. Computer simulation for these minimum distance estimators, accompanied by Cramér estimator, is performed and the function s(n)=a_0+a_1root n is fitted to the L_1-errors of f_n leading to the proportionality constant a1 determination. Further, (expected) L_1-consistency rate of Kolmogorov estimator under generalized assumptions based on asymptotic domination relation is studied. No usual continuity or differentiability conditions are needed.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10103 - Statistics and probability
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Metrika
ISSN
0026-1335
e-ISSN
1435-926X
Volume of the periodical
80
Issue of the periodical within the volume
2
Country of publishing house
DE - GERMANY
Number of pages
15
Pages from-to
243-257
UT code for WoS article
000393032400007
EID of the result in the Scopus database
2-s2.0-84991585239