Heavy tailed models: Bootstrapping the sample mean and stable dependence structure

When the sample comes from a distribution with infinite variance, the limiting distributions of the bootstrapped sample mean are classified, with broadest possible setting for the (nonrandom) scaling, the resample size, the mode of convergence (in law). The limiting distributions turn out to be infinitely divisible with possibly random Levy measure, depending on the resample size. An average-bootstrap algorithm is introduced which eliminates any randomness in the limiting distribution. It is shown that (on the average) the limiting distribution of the bootstrapped sample mean is stable if and only if the sample is taken from a distribution in the domain of (partial) attraction of a stable law.; The second half of the thesis addresses the problem of the conditional moments of stable vectors. Necessary and sufficient conditions are given for the linearity of regression on a stable vector; along with a sufficient condition for the finiteness of the conditional absolute moment when O {dollar}