What is the variability of the exchange rate of Euro to Australian dollar? Can we improve the use of the
electrocardiogram of a patient as a diagnostic tool for heart disease? A well-known limitation of the existing
statistical methods for answering these types of questions is that a small proportion of extreme observations
have the potential to lead to results that are more in agreement with the outliers than with bulk of the data. As
a consequence, the statistical analyses may lead to wrong conclusions. This project aims to develop new
methodologies to solve this problem for a large class of studies. Applications to stock market risk, exchange
rate, and diagnosis of heart diseases will illustrate the new methods.