Notes on consistency of some minimum distance estimators with simulation results
Result 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.
Keywords
Minimum distance estimatorsConsistencyKolmogorov distanceDegree of variations
The result's identifiers
Result code in IS VaVaI
Alternative codes found
RIV/68407700:21340/17:00304795
Result on the web
http://link.springer.com/article/10.1007%2Fs00184-016-0601-0
DOI - Digital Object Identifier
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
Jimp - 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
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)
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
Basic information
Result type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
OECD FORD
Statistics and probability
Year of implementation
2017