Tightness of M-Estimators for Multiple Linear Regression in Time for Multiple Linear Regression in Time Series

21 Pages Posted: 13 Jun 2016

See all articles by Soren Johansen

Soren Johansen

University of Copenhagen - Department of Economics; Aarhus University - CREATES

Bent Nielsen

University of Oxford - Nuffield Department of Medicine

Date Written: May 28, 2016

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

JEL Classification: 22

Suggested Citation

Johansen, Soren and Nielsen, Bent, Tightness of M-Estimators for Multiple Linear Regression in Time for Multiple Linear Regression in Time Series (May 28, 2016). Univ. of Copenhagen Dept. of Economics Discussion Paper No. 16-05, Available at SSRN: https://ssrn.com/abstract=2794851 or http://dx.doi.org/10.2139/ssrn.2794851

Soren Johansen (Contact Author)

University of Copenhagen - Department of Economics ( email )

Ă˜ster Farimagsgade 5
Bygning 26
1353 Copenhagen K.
Denmark

Aarhus University - CREATES ( email )

Nordre Ringgade 1
Aarhus, DK-8000
Denmark

Bent Nielsen

University of Oxford - Nuffield Department of Medicine ( email )

New Road
Oxford, OX1 1NF
United Kingdom

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