Mathematical Sciences: Limit Theorems in Statistics
{'Code': '03040107', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Peter Arzberger', 'PO_EMAI': None, 'PO_PHON': None}
This project contains two major themes:  a "complete"                       solution of the L-statistics problem, and empirical processes.                       Specific topics to be studied include:  (1) necessary and                  sufficient conditions for asymptotic normality and for                          stochastic compactness of (a) classical L-statistics, (b) L-                    statistics, L-statistics in which a fixed fraction of extreme                   order statistics are trimmed and (c) L-statistics in which a                    vanishingly small fraction of extreme order statistics are                      trimmed.  (2) studentization in each of these cases.  (3)                       providing a studentized version of a trimmed mean, with                         vanishingly small trimming fraction, that is approximately and                  asymptotically standard normal whenever the underlying                          observations are in the domain of attraction of any stable law.                 (4) extending the previous result to general L-statistics.  (5)                 extending all above results to include random trimming.  (6)                    providing a probabilistic representation of all possible limiting               distributions of L-statistics in cases (a), (b) and (c), and a                  characterization of when each obtains.  (7) extending all                       results above to generalized U-statistics.  (8) limit theorems                  for the Kaplan-Meier estimator process and corresponding                        cumulative hazard estimator process under independent but not                   identically distributed censoring distributions.  (9) exponential               inequalities for the weighted empirical processes of independent                but not identicallly distributed rv's.  (10) the determination of               Piitman efficiency of estimators of sufficient complexity that a                technique like bootstrapping is essential to apply them to a                    specific data set.
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{'Code': '1263', 'Text': 'PROBABILITY'}
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