An algorithm suggested by Hendry (1999) for estimation in a regression with more regressors than observations, is analyzed with the purpose of finding an estimator that is robust to outliers and structural breaks.  This estimator is an example of a one-step M-estimator based on Huber's skip...

The Forward Search is an iterative algorithm concerned with detection of outliers and other unsuspected structures in data. This approach has been suggested, analysed and applied for regression models in the monograph Atkinson and Riani (2000). An asymptotic analysis of the Forward Search is...

An algorithm suggested by Hendry (1999) for estimation in a regression with more regressors than observations, is analyzed with the purpose of finding an estimator that is robust to outliers and structural breaks. This estimator is an example of a one-step M-estimator based on Huber's skip...

A uniform weak consistency theory is presented for the marked and weighted empirical distribution function of residuals. New and weaker sufficient conditions for uniform consistency are derived. The theory allows for a wide variety of regressors and error distributions. We apply the theory to...

An extended and improved theory is presented for marked and weighted empirical processes of residuals of time series regressions. The theory is motivated by 1-step Huber-skip estimators, where a set of good observations are selected using an initial estimator and an updated estimator is found by...

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...

The Forward Search Algorithm is a statistical algorithm for obtaining robust estimators of regression coefficients in the presence of outliers. The algorithm selects a succession of subsets of observations from which the parameters are estimated. The present note shows how the theory of...

The paper by Atkinson, Riani and Ceroli, henceforth ARC, is concerned with detection of outliers and unsuspected structures which is rather important in practice.  This is done through a Forward Search Algorithm.  The statistical analysis of such algorithms poses many challenging problems, and...

The Forward Search is an iterative algorithm concerned with detection of outliers and other unsuspected structures in data.  This approach has been suggested, analysed and applied for regression models in the monograph Atkinson and Riani (2000).  An asymptotic analysis of the Forward Search is...

When analysing macroeconomic data it is often of relevance to allow for structural breaks in the statistical analysis. In particular, cointegration analysis in the presence of structural breaks could be of interest. We propose a cointegration model with piecewise linear trend and known break...