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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 |
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Journal | Econometric Theory |
Volume | 35 |
Issue | 3 |
Pages (from-to) | 653-683 |
Number of pages | 31 |
ISSN | 0266-4666 |
DOIs | |
Publication status | Published - Jun 2019 |
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