Some Integrated Squared Error Procedures for Multivariate Normal Data

Two estimation procedures for the parameters of the multivariate normal distribution, based on the sample characteristic function and having an equivalent basis in terms of density estimation, are presented. The procedures depend on a user-specified index, variation of which produces a response surface in the parameter estimates, allowing for an informal sensitivity analysis of the data and tentative working model. The estimators are robust, relatively efficient at the multivariate normal, easy to compute and use, useful in identifying potential outliers and inconsistencies in statistical assumptions, and are directly applicable to structured data such as designed experiments. Several illustrations are provided