ABSTRACT
This chapter considers the estimation of location and scale. A large number of useful estimators can be defined as or approximated by M-estimators. For normal observations, the best linear unbiased estimator (BLUE) is the maximum likelihood estimator and is therefore optimal in the sense that, it has the smallest possible variance among all unbiased estimators. This implies that for Gaussian long-memory processes, the sample mean is almost optimal. In practice however, deviations from the normal distribution are expected. The sample mean is very sensitive to outliers and other deviations from normality. The variance of the BLUE was derived by R. K. Adenstedt. Jan Beran considered the special case of short-memory processes where the sum of all correlations is zero.
