Improved linear regression with process applications

Citation

Holcomb, Tyler Reed (1993) Improved linear regression with process applications. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/pfq3-3n74. https://resolver.caltech.edu/CaltechETD:etd-08272007-140750

Abstract

This work examines biased linear regressors. Two major classes are identified: Bayesian estimators and restriction regressors. Both classes are useful for process applications, but the latter lack much of the unifying theory of the former. The properties of restriction regressors are examined and the characteristics of a "good" restriction regressor are expressed as a null hypothesis. Based on this characterization of "good," a novel restriction regressor is developed directly from the classical statistical concept of significance. This new method is called Significance Regression (SR). For scalar output problems, the popular Partial Least Squares algorithm (PLS) is a method for computing SR. For multiple output problems, SR yields a novel algorithm and PLS is sub-optimal.

SR is described using linear operator theory; this description allows facile generalization. SR is generalized for measurement error models and for robust regression methods. Analysis of these two extensions in turn provides insight an area that is currently dominated by useful heuristics with sparse mathematical grounding: scaling the data.

The theoretical results are illuminated by a variety of examples. First, several of the key points of the study are examined via simulation. Next, restriction regression is used in a robust inferential controller for a packed-bed react and for the modeling of cellular metabolism. Recommendations for implementing significance regression and suggestions for future research are provided.

Thesis Files