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Title: Tightness of M-estimators for multiple linear regression in time series Authors:  Bent Nielsen - University of Oxford (United Kingdom) [presenting]
Abstract: Tightness of a general M-estimator for multiple linear regression in time series is shown. 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.