Tightness of M-Estimators for Multiple Linear Regression in Time for Multiple Linear Regression in Time Series
21 Pages Posted: 13 Jun 2016
Date Written: May 28, 2016
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
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