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|Title:||Inferences on high-dimensional data|
|Doctoral Committee Chair(s):||Simpson, Douglas G.|
|Department / Program:||Statistics|
|Degree Granting Institution:||University of Illinois at Urbana-Champaign|
|Abstract:||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.
|Rights Information:||Copyright 1990 Guo, Sha-Lin|
|Date Available in IDEALS:||2011-05-07|
|Identifier in Online Catalog:||AAI9114251|