On Solving Robust and Generalized Linear Regression Problems.
Abstract
Many researchers employ mathematical models. Most models contain parameters, which may be chosen to make the model fit the available data as well as possible (in a sense that depends on the model). In this paper we consider the problem of choosing the parameters for a common class of models in which the desired parameter vector minimizes an (unconstrained) objective function. We briefly give some examples of such problems, then discuss ways to exploit the common structure that these problems share. THis leads us to discussing strategies for solving general unconstrained minimization problems and to point out the advantages of using a so-called 'model/trust-region approach,' wherein the change made in the current parameter estimate is chosen so as to approximately minimize a local model of the objective function on an estimate of the region about the current iterate where this local model is reliable. For problems in which the residual vector r(x) is a nonlinear function of x, we recommend generalizations of some techniques that have proven worthwhile in nonlinear least-squares problems in which the optimal residual vector r(x*) may be either large or small.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1979
- Accession Number
- ADA079735
Entities
People
- David M. Gay
Organizations
- University of Wisconsin–Madison