ON NON-REGULAR ESTIMATION, MINIMUM VARIANCE BOUNDS AND THE PEARSON TYPE III DISTRIBUTION.
Abstract
This project concerns general investigations on the theory of non-regular estimation and particular investigations leading to asymptotically efficient estimators for the parameters of the Pearson Type III distribution and also for other distributions, including Types I and V of the Pearson system, the Weibull distribution and a generalization of the gamma distribution. In all of these examples the difficulty is in estimating the location parameter. In each case for a non-trivial subset of the parameter space, standard techniques, including those derived specifically for the non-regular case, for determining a lower bound on the variance of an unbiased estimator result in an inequality which states that the variance of all such estimators is non-negative. New bounds, which yield uniformly non-trivial results, have been constructed. These have been applied to the above examples. Some suggestions for constructing estimators whose variance achieves at least the order of magnitude of these bounds are offered. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1965
- Accession Number
- AD0622274
Entities
People
- A. J. Truelove
- A. M. Glinski
- M. V. Johns Jr.
- P. B. Mundle
- W. R. Blischke