“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.
Antle, Charles E.
Baird, Thomas B.
Webb, William H.
Sauer, Harry J., Jr., 1935-2008
Mathematics and Statistics
M.S. in Applied Mathematics
University of Missouri at Rolla
vi, 37 pages
© 1964 Gerald N. Haas, All rights reserved.
Thesis - Open Access
Print OCLC #
Link to Catalog Record
Haas, Gerald Nicholas, "A study of methods for estimating parameters in the model y(t) = A₁e-p₁t + A₂e-p₂t + ϵ" (1964). Masters Theses. 5684.