Mathematical Sciences: Probability, Statistics and          Functional Analysis
{'Code': '03040107', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Peter Arzberger'}
The principal investigator will continue his investigation                 of the use of Vapnik-Cervonenkis (V-C) classes in estimation of                 multivariate distributions.  The validity of the estimates is                   judged from the deviation of the estimated from the true                        probability for some collection of regions C.  A class C is                     called a V-C class for m if it "shatters" no set of m points.  By               definition a class C shatters a set F if every subset of F can be               viewed as the intersection of F with some element of C.  The                    principal investigator has shown before that the deviation of the               estimates from the true probability multiplied by square root of                n, approaches a normal limit for all possible distributions only                if C is a V-C class.  This theoretical result will be made                      practical and useful by finding tight bounds on the deviations                  for fixed n and designing computationally efficient methods.                    Other applications relate to tests for normality and                            classification problems.
{'FirstName': 'Richard', 'LastName': 'Dudley', 'EmailAddress': 'rmd@math.mit.edu', 'StartDate': '07/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Massachusetts Institute of Technology', 'CityName': 'Cambridge', 'ZipCode': '021394301', 'PhoneNumber': '6172531000', 'StreetAddress': '77 MASSACHUSETTS AVE', 'CountryName': 'United States', 'StateName': 'Massachusetts', 'StateCode': 'MA'}
{'Code': '1263', 'Text': 'PROBABILITY'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1988&All=true', 'xml': '8803305.xml'}