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.
I: Econometric Theory, Bind 35, Nr. 3, 2019, s. 653-683.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Boundedness of M-estimators for linear regression in time series
AU - Johansen, Søren
AU - Nielsen, Bent
PY - 2019
Y1 - 2019
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
VL - 35
SP - 653
EP - 683
JO - Econometric Theory
JF - Econometric Theory
SN - 0266-4666
IS - 3
ER -
ID: 209600192