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Simpson, Douglas G. Guo, Sha-Lin 2011-05-07T14:16:46Z 2011-05-07T14:16:46Z 10000-01-01 1990 "Dimension reduction techniques are important in the problem of regression and prediction when the nominal number of predicting variables is greater than the number of observations. Two methods, principal components analysis (PCA) and partial least squares (PLS), are used for regression and classification. We show that the null distribution of the PLS ""f-test"" statistic, which is obtained from one factor PLS regression, depends heavily on the design. A simulation method is suggested to compute the appropriate significant level of the ""f-test"". Some of the statistical properties of the composite dimensional reduction procedures are derived." In classification, it is shown that the linear discriminant rule based on PLS in the two groups case corresponds to assigning the covariance structure which is spherical. This suggests that some improvement might be possible by more flexible modelling of the covariance structure. We use a time series model for the covariance. This leads to a parametric quadratic classifier. The approach appears to be useful in determining which components are responsible for the classification. Made available in DSpace on 2011-05-07T14:16:46Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9114251.pdf: 2638665 bytes, checksum: 747091a3c4dc6c9b4a6401c0def9bfa2 (MD5) Previous issue date: 1990 Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T15:04:57Z Item is restricted indefinitely. Restriction data tranferred 2014-07-01T11:31:04-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission ETDs are only available to UIUC Users without author permission U of I Only AAI9114251 (UMI)AAI9114251 http://hdl.handle.net/2142/23507 eng Copyright 1990 Guo, Sha-Lin Statistics Inferences on high-dimensional data text Statistics University of Illinois at Urbana-Champaign Dissertation Ph.D. Statistics