Boundedness of M-estimators for linear regression in time series

Søren Johansen; Bent Nielsen

doi:10.1017/S0266466618000257

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.

Original language	English
Journal	Econometric Theory
Volume	35
Issue number	3
Pages (from-to)	653-683
ISSN	0266-4666
DOIs	https://doi.org/10.1017/S0266466618000257
Publication status	Published - 1 Jun 2019

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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.",

author = "S{\o}ren Johansen and Bent Nielsen",

year = "2019",

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

AU - Johansen, Søren

AU - Nielsen, Bent

PY - 2019/6/1

Y1 - 2019/6/1

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.

U2 - 10.1017/S0266466618000257

DO - 10.1017/S0266466618000257

M3 - Journal article

SN - 0266-4666

VL - 35

SP - 653

EP - 683

JO - Econometric Theory

JF - Econometric Theory

IS - 3

ER -

Boundedness of M-estimators for linear regression in time series

Abstract

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