Graduate Thesis Or Dissertation

 

Recursive least-squares smoothing with constant or factorial weights Public Deposited

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/f7623g139

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  • This thesis develops recursion formulas for least-squares data smoothing with regard to four classes of functions: linear, quadratic, exponential and trigonometric, which in a linear fashion involve 2, 3, 2 and 2 parameters respectively. The term recursion implies here that the estimates for the parameters of the preceding fit are taken to summarize all past data and are used along with the new observation to yield new estimates of the parameters. Results for constant weights are given in all cases and in addition factorial weights are considered in the linear and quadratic cases, which yield the simplest results. In the linear case an effort is made to lead the reader to some sort of intuitive acceptance of the precedents set by Levine [1] with regard to the special forms of linear and quadratic functions adopted for the fitting procedure. As may be noted in the smoothing equations for each of the four cases, the change in a parameter is always proportional to the difference between the new observation and the corresponding prediction. Following the trigonometric case an example is given which is intended to illustrate the usefulness of least-squares recursion formulas in terms of the considerable saving of computational labor.
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