Instrumental weighted variables under heteroscedasticity Part I - Consistency

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

Instrumental weighted variables under heteroscedasticity Part I - Consistency

Original language description

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.

Czech name

—

Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

50201 - Economic Theory

Project

<a href="/en/project/GA13-01930S" target="_blank" >GA13-01930S: Robust methods for nonstandard situations, their diagnostics and implementations</a><br>

Continuities

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

Publication year

2017

Confidentiality

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

Name of the periodical

Kybernetika

ISSN

0023-5954

e-ISSN

—

Volume of the periodical

53

Issue of the periodical within the volume

1

Country of publishing house

CZ - CZECH REPUBLIC

Number of pages

25

Pages from-to

1-25

UT code for WoS article

000400203500001

EID of the result in the Scopus database

2-s2.0-85017012016