Moment Estimation Using Extreme Value Methods

Abstract: The thesis is composed of three papers, all dealing with the application of extreme value methods to the problem of moment estimation for heavy-tailed distributions.

In Paper A, an asymptotically normally distributed estimate for the expected value of a positive random variable with infinite variance is introduced. Its behavior relative to estimation using the sample mean is investigated by simulations. An example of how to apply the estimate to file-size measurements on Internet traffic is also shown.

Paper B extends the results of Paper A to a situation where the variables are m-dependent. It is shown how this method can be applied for estimating covariances and be put to use as a diagnostic tool for estimating the order of an ARMA-processes with heavy-tailed innovations.

Paper C further extends the methodology to the case of regression through the origin with heteroscedastic errors. In a simulation study, the estimate is compared to some standard alternatives and used for estimating the population total in a superpopulation sampling framework.