| Dr. Hasan Hamdan, 2 April 2007 |
| Approximating and
Estimating Infinite Variance Mixtures of Normals |
ABSTRACT: The talk will address three questions related to the problem of estimating infinite variance mixtures of normals, VMN. First, given an infinite variance mixture of normals with a known mixing measure, how do we approximate its density up to a specified tolerance level? A constructive proof of how to guarantee that a finite variance mixture of normals is uniformly close to a given infinite variance mixture distribution is presented. Second, in the case of an unknown mixing measure, how do we estimate the density of the VMN from a random sample of points? We present one approach based on minimizing the squared weighted distance between the estimated density and the approximated density over a fixed grid of X values. The possibility of extending these techniques to infinite variance-mean mixtures of normals or multivariate mixtures of normals will be outlined. Finally, applications of the method are made in modeling the continuously compounded return of stock prices. Modeling this ratio with this method proves promising in comparison with other existing techniques. |
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