Existence, Consistency and Computer Simulation for Selected Variants of Minimum Distance Estimators

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/68407700:21340/18:00316345

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Existence, Consistency and Computer Simulation for Selected Variants of Minimum Distance Estimators

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Existence, Consistency and Computer Simulation for Selected Variants of Minimum Distance Estimators

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10103 - Statistics and probability

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Kybernetika

ISSN

0023-5954

e-ISSN

—

Svazek periodika

54

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

15

Strana od-do

336-350

Kód UT WoS článku

000435168400008

EID výsledku v databázi Scopus

2-s2.0-85047380840