University of Illinois Urbana-Champaign

Inferences on high-dimensional data

Guo, Sha-Lin

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Description

Title
Inferences on high-dimensional data
Author(s)
Guo, Sha-Lin
Issue Date
1990
Doctoral Committee Chair(s)
Simpson, Douglas G.
Department of Study
Statistics
Discipline
Statistics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Statistics
Language
eng
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.
Type of Resource
text
Permalink
http://hdl.handle.net/2142/23507
Copyright and License Information
Copyright 1990 Guo, Sha-Lin

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