Instrumental weighted variables under heteroscedasticity Part I - Consistency

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11230%2F17%3A10360472" target="_blank" >RIV/00216208:11230/17:10360472 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.14736/kyb-2017-1-0001" target="_blank" >http://dx.doi.org/10.14736/kyb-2017-1-0001</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.14736/kyb-2017-1-0001" target="_blank" >10.14736/kyb-2017-1-0001</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Instrumental weighted variables under heteroscedasticity Part I - Consistency

Popis výsledku v původním jazyce

The proof of consistency instrumental weighted variables, the robust version of the classical instrumental variables is given. It is proved that all solutions of the corresponding normal equations are contained, with high probability, in a ball, the radius of which can be selected - asymptotically - arbitrarily small. Then also root n-consistency is proved. An extended numerical study (the Part II of the paper) offers a picture of behavior of the estimator for finite samples under various types and levels of contamination as well as various extent of heteroscedasticity. The estimator in question is compared with two other estimators of the type of &quot;robust instrumental variables&quot; and the results indicate that our estimator gives comparatively good results and for some situations it is better. The discussion on a way of selecting the weights is also offered. The conclusions show the resemblance of our estimator with the M-estimator with Hampel&apos;s psi-function. The difference is that our estimator does not need the studentization of residuals (which is not a simple task) to be scale- and regression-equivariant while the M-estimator does. So the paper demonstrates that we can directly compute - moreover by a quick algorithm (reliable and reasonably quick even for tens of thousands of observations) - the scale- and the regression-equivariant estimate of regression coefficients.

Název v anglickém jazyce

Instrumental weighted variables under heteroscedasticity Part I - Consistency

Popis výsledku anglicky

The proof of consistency instrumental weighted variables, the robust version of the classical instrumental variables is given. It is proved that all solutions of the corresponding normal equations are contained, with high probability, in a ball, the radius of which can be selected - asymptotically - arbitrarily small. Then also root n-consistency is proved. An extended numerical study (the Part II of the paper) offers a picture of behavior of the estimator for finite samples under various types and levels of contamination as well as various extent of heteroscedasticity. The estimator in question is compared with two other estimators of the type of &quot;robust instrumental variables&quot; and the results indicate that our estimator gives comparatively good results and for some situations it is better. The discussion on a way of selecting the weights is also offered. The conclusions show the resemblance of our estimator with the M-estimator with Hampel&apos;s psi-function. The difference is that our estimator does not need the studentization of residuals (which is not a simple task) to be scale- and regression-equivariant while the M-estimator does. So the paper demonstrates that we can directly compute - moreover by a quick algorithm (reliable and reasonably quick even for tens of thousands of observations) - the scale- and the regression-equivariant estimate of regression coefficients.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

50201 - Economic Theory

Projekt

<a href="/cs/project/GA13-01930S" target="_blank" >GA13-01930S: Robustní procedury pro nestandardní situace, jejich diagnostika a implementace</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

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

53

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

25

Strana od-do

1-25

Kód UT WoS článku

000400203500001

EID výsledku v databázi Scopus

2-s2.0-85017012016