Mathematical Sciences: Inference Problems in Multivariate   Statistical 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}
This research is concerned with problems of inference in                classical multivariate procedures such as multivariate analysis                 of variance, discriminant analysis , principal components                       analysis, and canonical correlations analysis.  The problems                    posed are of two main types.  One involves problems in estimating               canonical correlations and the eigenstructures of parameter                     matrices arising in multivariate analysis of variance.  The                     investigators propose to apply decision-theoretic concepts and to               evaluate the properties and behavior of estimates based on these                concepts.  The second type of problem to be investigated involves               hypothesis testing.  Widely used tests in multivariate analysis                 are ones which hypothesize the equality of a subset of the                      characteristic roots of a parameter matrix.  No small sample                    properties (unbiasedness, monotonicity of the power functions,                  admissibility, etc.) are known for common tests, including the                  likelihood ratio test.  The usefulness of the bootstrapping                     technique in problems of inference in multivariate analysis will                be investigated.                                                                        Classical multivariate statistical procedures are                       characterized by assumptions of linearity, independence and                     normality.  These procedures are widely used throughout the                     sciences to analyze experimental and observational data.  The                   statistical procedures for making some of the estimates used in                 these multivariate analyses are crude and, therefore, improving                 them may have a significant impact on the conclusions scientists                draw about relationships between measurements.  Also in this                    setting, our current knowledge about the performance of                         statistical decision making procedures applies strictly to                      experiments that are repeated a very large number of times.                     Since replicating experiments is usually expensive, it is                       typically done with low frequency.  The research into the                       performance of statistical decision making procedures when the                  number of replicates is small is expected to provide valuable                   information and insight to a broad spectrum of the scientific                   community.
{'FirstName': 'Robb', 'LastName': 'Muirhead', 'PI_MID_INIT': 'J', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Robb J Muirhead', 'EmailAddress': 'robb@stat.lsa.umich.edu', 'NSF_ID': '000113998', 'StartDate': '07/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
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{'Code': '1269', 'Text': 'STATISTICS'}
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