  Linear regression with normally distributed errors - including particular
cases such as ANOVA, Student's t-test or location-scale inference - is a widely
used statistical procedure. In this case the ordinary least squares estimator
possesses remarkable properties but is very sensitive to outliers. Several
robust alternatives have been proposed, but there is still significant room for
improvement. This paper thus proposes an original method of estimation that
offers the best efficiency simultaneously in the absence and the presence of
outliers, both for the estimation of the regression coefficients and the scale
parameter. The approach first consists in broadening the normal assumption of
the errors to a mixture of the normal and the filtered-log-Pareto (FLP), an
original distribution designed to represent the outliers. The
expectation-maximization (EM) algorithm is then adapted and we obtain the N-FLP
estimators of the regression coefficients, the scale parameter and the
proportion of outliers, along with probabilities of each observation being an
outlier. The performance of the N-FLP estimators is compared with the best
alternatives in an extensive Monte Carlo simulation. The paper demonstrates
that this method of estimation can also be used for a complete robust
inference, including confidence intervals, hypothesis testing and model
selection.
