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Boundedness of M-estimators for linear regression in time series

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Boundedness of M-estimators for linear regression in time series. / Johansen, Søren; Nielsen, Bent.

In: Econometric Theory, Vol. 35, No. 3, 06.2019, p. 653-683.

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Johansen, Søren ; Nielsen, Bent. / Boundedness of M-estimators for linear regression in time series. In: Econometric Theory. 2019 ; Vol. 35, No. 3. pp. 653-683.

Bibtex

@article{e9e1c0c6dda94816a7110262a40e008c,
title = "Boundedness of M-estimators for linear regression in time series",
abstract = "We show boundedness in probability uniformly in sample size of a general M-estimator for multiple linear regression in time series. The positive criterion function for the M-estimator is assumed lower semicontinuous and sufficiently large for large argument. Particular cases are the Huber-skip and quantile regression. Boundedness requires an assumption on the frequency of small regressors. We show that this is satisfied for a variety of deterministic and stochastic regressors, including stationary and random walks regressors. The results are obtained using a detailed analysis of the condition on the regressors combined with some recent martingale results.",
keywords = "CONSISTENCY, LIMIT THEORY, MARTINGALES, SQUARES",
author = "S{\o}ren Johansen and Bent Nielsen",
year = "2019",
month = jun,
doi = "10.1017/S0266466618000257",
language = "English",
volume = "35",
pages = "653--683",
journal = "Econometric Theory",
issn = "0266-4666",
publisher = "Cambridge University Press",
number = "3",

}

RIS

TY - JOUR

T1 - Boundedness of M-estimators for linear regression in time series

AU - Johansen, Søren

AU - Nielsen, Bent

PY - 2019/6

Y1 - 2019/6

N2 - We show boundedness in probability uniformly in sample size of a general M-estimator for multiple linear regression in time series. The positive criterion function for the M-estimator is assumed lower semicontinuous and sufficiently large for large argument. Particular cases are the Huber-skip and quantile regression. Boundedness requires an assumption on the frequency of small regressors. We show that this is satisfied for a variety of deterministic and stochastic regressors, including stationary and random walks regressors. The results are obtained using a detailed analysis of the condition on the regressors combined with some recent martingale results.

AB - We show boundedness in probability uniformly in sample size of a general M-estimator for multiple linear regression in time series. The positive criterion function for the M-estimator is assumed lower semicontinuous and sufficiently large for large argument. Particular cases are the Huber-skip and quantile regression. Boundedness requires an assumption on the frequency of small regressors. We show that this is satisfied for a variety of deterministic and stochastic regressors, including stationary and random walks regressors. The results are obtained using a detailed analysis of the condition on the regressors combined with some recent martingale results.

KW - CONSISTENCY

KW - LIMIT THEORY

KW - MARTINGALES

KW - SQUARES

UR - http://www.scopus.com/inward/record.url?scp=85052958397&partnerID=8YFLogxK

U2 - 10.1017/S0266466618000257

DO - 10.1017/S0266466618000257

M3 - Journal article

AN - SCOPUS:85052958397

VL - 35

SP - 653

EP - 683

JO - Econometric Theory

JF - Econometric Theory

SN - 0266-4666

IS - 3

ER -