Tightness of M-estimators for multiple linear regression in time for multiple linear regression in time series

Soren Johansen and Bent Nielsen
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Bent Nielsen: Department of Economics, Nuffield College

No 16-05, Discussion Papers from University of Copenhagen. Department of Economics

Abstract: We show tightness of a general M-estimator for multiple linear regression in time series. The positive criterion function for the M-estimator is assumed lower semi-continuous and sufficiently large for large argument: Particular cases are the Huber-skip and quantile regression. Tightness requires an assumption on the frequency of small regressors. We show that this is satis?ed for a variety of deterministic and stochastic regressors, including stationary an random walks regressors. The results are obtained using a detailed analysis of the condition on the regressors combined with some recent martingale results.

Keywords: M-estimator; robust statistics; martingales; Huber-skip; quantile estimation. (search for similar items in EconPapers)
Pages: 21 pages
Date: 2016-06-10
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-net
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Persistent link: https://EconPapers.repec.org/RePEc:kud:kuiedp:1605

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