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  • Søren Johansen (a1) and Bent Nielsen (a2)

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.

Corresponding author
*Address correspondence to Bent Nielsen, Nuffield College & Department of Economics, University of Oxford & Programme for Economic Modelling Nuffield College, Oxford, OX1 1NF, UK; e-mail:
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The first author is grateful to CREATES - Center for Research in Econometric Analysis of Time Series (DNRF78), funded by the Danish National Research Foundation, and to Steffen Lauritzen for useful comments.

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Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
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