Consistent Estimation of Variance Parameters from Many Small Samples with Different Means.
Abstract
Where sets of observations are normally distributed with variances related to the mean of each set, the mean values become nuisance parameters when we wish to pool information about the variances from a large number of sets of information. This paper considers the problem of obtaining consistent estimators of the variance parameters where no assumptions or prior knowledge are available about the mean values. When the variance is proportional to the square of the mean we obtain an estimator for the constant of proportionality which is always consistent, by a marginal likelihood approach, but this method cannot be generalized to other variance functions. Integrated, modified, and partial conditional likelihood methods are investigated for this example and suggest methods for the general example when the standard deviation is small compared with the mean. The partial conditional likelihood method may be a useful general method of eliminating nuisance parameters in problems where the methods proposed by Kalbfleisch and Sprott (1970) are not applicable. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1979
- Accession Number
- ADA078227
Entities
People
- Gillian M. Raab
- Nicholas P. Jewell
Organizations
- Princeton University