Iterated one-step Huber-skip M-estimators are considered for regression problems. Each one-step estimator is a re-weighted least squares estimators with zero/one weights determined by the initial estimator and the data. The asymptotic theory is given for iteration of such estimators using a...

This paper derives the exact distribution of the maximum likelihood estimator of a first order linear autoregression with exponential innovations. We show that even if the process is stationary, the estimator is $T$-consistent, where $T$ is the sample size. In the unit root case the estimator is...

Estimated characteristic roots in stationary auto-regressions are shown to give rather noisy information about their population equivalents. This is remarkable given the central role of the characteristic roots in the theory of autoregressive processes. In the asymptotic analysis the problems...

We review recent asymptotic results on some robust methods for multiple regression. The regressors include stationary and non-stationary time series as well as polynomial terms. The methods include the Huber-skip M-estimator, 1-step Huber-skip M-estimators, in particular the Impulse Indicator...

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...