A study of methods for estimating parameters in the model y(t) = A₁e^-p₁t + A₂e^-p₂t + ϵ

Author

Gerald Nicholas Haas

Abstract

“In this study, methods for estimating the unknown parameters A₁, A₂, p₁, and p₂ in the model
y(t) = A₁e^-p₁t + A₂e^-p₁t + ϵ
where ϵ ~ N(0, σ) are investigated. In the model investigated, A₁, A₂, p₁, and p₂ are positive.

Four methods, one non-iterative method and three iterative methods, for estimating parameters in this model are investigated. The non-iterative method is known as Prony's Method. The three iterative methods are (1) the Modified Gauss Iterative Method, (2) a combination of the Gauss Iterative Method and the Method of Least Squares, and (3) the Method of Steepest Descent. A method for obtaining starting values is presented for the iterative methods. This method is a graphical means sometimes used for estimating the unknown parameters in this model. Iterative methods (1) and (2) proved superior to this graphical method.

The methods are Investigated in two ways. First, the parameters are estimated from data generated from the exact model, that is, the model containing the exact parameters. These data have eight significant figures of accuracy. Secondly, random errors are added to these exact data. These random errors are distributed as N(0, σ₂). The variance of the random error is varied giving different error levels. At each error level, the methods are Investigated for fifty different sets of random errors. The same starting values were used for each set of errors.

The Modified Gauss Iterative Method proved best for errorless data. The combination of the Gauss Iterative Method and the Method of Least Squares proved to be the best method for improving starting values for data with random error"--Abstract, pages ii-iii.

Advisor(s)

Antle, Charles E.

Committee Member(s)

Baird, Thomas B.
Webb, William H.
Sauer, Harry J., Jr., 1935-2008

Department(s)

Mathematics and Statistics

Degree Name

M.S. in Applied Mathematics

Comments

Pages v and vi are in reverse order in the manuscript.

Publisher

University of Missouri at Rolla

Publication Date

1964

Pagination

vi, 37 pages

Note about bibliography

Includes bibliographical references (page 33).

Rights

© 1964 Gerald N. Haas, All rights reserved.

Document Type

Thesis - Open Access

File Type

text

Language

English

Thesis Number

T 1605

Print OCLC #

9537108

Recommended Citation

Haas, Gerald Nicholas, "A study of methods for estimating parameters in the model y(t) = A₁e^-p₁t + A₂e^-p₂t + ϵ" (1964). Masters Theses. 5684.
https://scholarsmine.mst.edu/masters_theses/5684