EIV regression with bounded errors in data: total 'least squares' with Chebyshev norm

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10419032" target="_blank" >RIV/00216208:11320/20:10419032 - isvavai.cz</a>

Alternative codes found

RIV/61384399:31140/20:00054768

Result on the web

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=gs5zqeEpuC" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=gs5zqeEpuC</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00362-017-0939-z" target="_blank" >10.1007/s00362-017-0939-z</a>

Result language

angličtina

Original language name

EIV regression with bounded errors in data: total 'least squares' with Chebyshev norm

Original language description

We consider the linear regression model with stochastic regressors and stochastic errors both in regressors and the dependent variable (&quot;structural EIV model&quot;), where the regressors and errors are assumed to satisfy some interesting and general conditions, different from traditional assumptions on EIV models (such as Deming regression). The most interesting fact is that we need neither independence of errors, nor identical distributions, nor zero means. The first main result is that the TLS estimator, where the traditional Frobenius norm is replaced by the Chebyshev norm, yields a consistent estimator of regression parameters under the assumptions summarized below. The second main result is that we design an algorithm for computation of the estimator, reducing the computation to a family of generalized linear-fractional programming problems (which are easily computable by interior point methods). The conditions under which our estimator works are (said roughly): it is known which regressors are affected by random errors and which are observed exactly; that the regressors satisfy a certain asymptotic regularity condition; all error distributions, both in regressors and in the endogenous variable, are bounded in absolute value by a common bound (but the bound is unknown and is estimated); there is a high probability that we observe a family of data points where the errors are close to the bound. We also generalize the method to the case that the bounds of errors in the dependent variable and regressors are not the same, but their ratios are known or estimable. The assumptions, under which our estimator works, cover many settings where the traditional TLS is inconsistent.

Czech name

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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

10103 - Statistics and probability

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)

Publication year

2020

Confidentiality

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

Name of the periodical

Statistical Papers

ISSN

0932-5026

e-ISSN

—

Volume of the periodical

61

Issue of the periodical within the volume

1

Country of publishing house

DE - GERMANY

Number of pages

23

Pages from-to

279-301

UT code for WoS article

000521495900015

EID of the result in the Scopus database

2-s2.0-85026556619