Mathematical Sciences: Limit Theorems for Sums and Extremes
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{'SignBlockName': 'Peter Arzberger', 'PO_EMAI': None, 'PO_PHON': None}
This research will investigate limit theorems for trimmed                  sums and self normalizing sums.  Limit theorems for sums of                     random variables have been of great interest in probability                     theory for both their mathematical beauty and their enormous                    potential for applications.  Major such application has been the                use of Central Limit Theorem for estimation of the mean.  The                   average of the observed values viz. the sample mean is generally                a good estimator of this.  However, it needs to be "trimmed"                    occasionally if the data is contaminated by outliers.  The limit                theory of such trimmed sums becomes quite complex, especially if                the trimming is not fixed.  If the normalizing constants are                    determined by the sample as well then the sums are called self                  normalizing.  Self normalizing has great application potential                  since it requires minimum assumptions on the distribution of the                sample.
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