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An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions, 2
| Content Provider | NASA Technical Reports Server (NTRS) |
|---|---|
| Author | Peters Jr., B. C. Walker, H. F. |
| Copyright Year | 1976 |
| Description | The problem of obtaining numerically maximum likelihood estimates of the parameters for a mixture of normal distributions is addressed. In recent literature, a certain successive approximations procedure, based on the likelihood equations, is shown empirically to be effective in numerically approximating such maximum-likelihood estimates; however, the reliability of this procedure was not established theoretically. Here, a general iterative procedure is introduced, of the generalized steepest-ascent (deflected-gradient) type, which is just the procedure known in the literature when the step-size is taken to be 1. With probability 1 as the sample size grows large, it is shown that this procedure converges locally to the strongly consistent maximum-likelihood estimate whenever the step-size lies between 0 and 2. The step-size which yields optimal local convergence rates for large samples is determined in a sense by the separation of the component normal densities and is bounded below by a number between 1 and 2. |
| File Size | 15064019 |
| Page Count | 39 |
| File Format | |
| Alternate Webpage(s) | http://archive.org/details/NASA_NTRS_Archive_19760019841 |
| Archival Resource Key | ark:/13960/t2q57cs5h |
| Language | English |
| Publisher Date | 1976-02-01 |
| Access Restriction | Open |
| Subject Keyword | Statistics And Probability Statistical Analysis Iterative Solution Probability Theory Distribution Functions Ntrs Nasa Technical Reports Server (ntrs) Nasa Technical Reports Server Aerodynamics Aircraft Aerospace Engineering Aerospace Aeronautic Space Science |
| Content Type | Text |
| Resource Type | Technical Report |
