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

Soren Johansen and Bent Nielsen ()
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Bent Nielsen: Nuffield College & Department of Economics, University of Oxford & Institute for New Economic Thinking at the Oxford Martin School, Postal: Nuffield College, Oxford OX1 1NF, UK

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

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 satisfied 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)
JEL-codes: C22 (search for similar items in EconPapers)
Pages: 20
Date: 2016-05-28
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
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