Method of Moments as the Least Squares Solution for Fitting a Polynomial.
Abstract
Methods of moments has been used frequently and effectively in our previous research for developing theories and methods of estimating the operating characteristics of the item response categories and ability distributions. It has been discovered that the method is quite useful, for fitting some curves to the set of observations, like maximum likelihood estimates, to the unobserved, conditional density function of which only the first few moments are estimated, and to the resultant, estimated density function of ability. It has also been discovered that polynomials are useful as functions to fit in applying the method of moments, with their unrestricted nature, regardless of the fact that there always is a possibility that they produce negative values for the estimated density. In the present paper, it is pointed out that a polynomial fitted by the method of moments is the same polynomial produced by the least squares principle. Using some examples, the two processes, i.e., the method of moments and the lest squares solution, are compared. It is pointed out that, in general, the method of moments provides us with a simpler process and a more accurate result, than the least squares method, when the computer work is involved. The importance of using the appropriate interval in applying the method of moments, and the least squares method, is emphasized.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 16, 1979
- Accession Number
- ADA072357
Entities
People
- Fumiko Samejima
- Philip Livingston
Organizations
- University of Tennessee