Mathematical Sciences: Rotatability, Majorization, and      Applications to Design of Experiments
{'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}
In the statistical design of experiments rotatability is one of                 the many desirable characteristics of a response surface                        design.  Recent work has, for the first time, provided ways to                  measure "how rotatable" a design may be when it is not                          perfectly rotatable.  This had previously been assessed by the                  viewing of tediously obtained contour diagrams.  By appealing                   to matrix majorization arguments, a new and better criterion of                 rotatability can be obtained.  Moreover by adopting a new                       algebraic format for the response surface, this can be done in                  a way that makes it easy to extend results to any degree.  This                 new rotatability criterion can then be applied to solve                         specific response surface design problems.  This objectives of                  this research project in statistics are to provide a new                        improved way of measuring "how rotatable" a given response                      surface design is, and to use this criterion to solve various                   design problems in the response surface area.
{'FirstName': 'Norman', 'LastName': 'Draper', 'PI_MID_INIT': 'R', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Norman R Draper', 'EmailAddress': 'draper@stat.wisc.edu', 'NSF_ID': '000251183', 'StartDate': '07/01/1989', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Wisconsin-Madison', 'CityName': 'MADISON', 'ZipCode': '537151218', 'PhoneNumber': '6082623822', 'StreetAddress': '21 North Park Street', 'StreetAddress2': 'Suite 6301', 'CountryName': 'United States', 'StateName': 'Wisconsin', 'StateCode': 'WI', 'CONGRESSDISTRICT': '02', 'CONGRESS_DISTRICT_ORG': 'WI02', 'ORG_DUNS_NUM': '161202122', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF WISCONSIN SYSTEM', 'ORG_PRNT_DUNS_NUM': '041188822'}
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{'Code': '1269', 'Text': 'STATISTICS'}
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