Mathematical Sciences: Applications of Smoothing Splines forInference and Data Analysis
{'Code': '03040107', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Alan Izenman', 'PO_EMAI': None, 'PO_PHON': None}
The first part of this research develops valid confidence                  sets for functionals of a spline estimate and the estimated                     smoothing parameter.  Two approaches to confidence intervals are                to treat the bias of the estimate as a random variable or to                    replace the bias by an upper bound.  The first method yields                    short intervals that are accurate only in an average sense while                the second method gives longer conservative intervals.                          Confidence intervals for the smoothing spline are derived from                  the distribution of the cross-validation function.  The second                  part of this research applies spline methods to two ill-posed                   problems that arise in microscopy and soil science.  Both of                    these topcs are related to solving an integral equation with                    discrete and noisy data.  In this context, partial spline models                can compensate for boundary effects while certain experimental                  designs may imporve the resolution of the estimate.                                  This statistical research project addresses the general                    problem in data analysis of estimating a smooth function f, from                functionals of f that are observed with error.  Often a                         parametric form of f is unknown and it is important to consider                 nonparametric estimators of f.  This project focuses on one                     nonparametric estimator that has been successful over a diverse                 range of applications, a cross-validated smoothing spline.
{'FirstName': 'Douglas', 'LastName': 'Nychka', 'PI_MID_INIT': 'W', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Douglas W Nychka', 'EmailAddress': 'nychka@mines.edu', 'NSF_ID': '000191118', 'StartDate': '05/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'North Carolina State University', 'CityName': 'RALEIGH', 'ZipCode': '276950001', 'PhoneNumber': '9195152444', 'StreetAddress': '2601 WOLF VILLAGE WAY', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'North Carolina', 'StateCode': 'NC', 'CONGRESSDISTRICT': '02', 'CONGRESS_DISTRICT_ORG': 'NC02', 'ORG_UEI_NUM': 'U3NVH931QJJ3', 'ORG_LGL_BUS_NAME': 'NORTH CAROLINA STATE UNIVERSITY', 'ORG_PRNT_UEI_NUM': 'U3NVH931QJJ3'}
{'Name': None, 'CityName': None, 'StateCode': None, 'ZipCode': None, 'StreetAddress': None, 'CountryCode': None, 'CountryName': None, 'StateName': None, 'CountryFlag': None, 'CONGRESSDISTRICT': None, 'CONGRESS_DISTRICT_PERF': '""'}
[{'Code': '126900', 'Text': 'STATISTICS'}, {'Code': '127100', 'Text': 'COMPUTATIONAL MATHEMATICS'}]
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8715756.xml'}