Asymptotic efficiency of the Spearman estimator and characterizations of distributions
- 19 Downloads
The Spearman estimator is designed to be a nonparametric estimator for the expectation of a tolerance distribution. We characterize the one-parameter families of distributions (the parameter being the mean of the distribution) for which the Spearman estimator has asymptotic efficiency one. In particular, when the parameter indexes the location, the characterizing distribution is the logistic distribution. In any other case of efficiency one, the family of distributions is given by certain transformations of a logistic distribution.
Key words and phrasesAsymptotic efficiency Spearman estimator logistic family characterization
Unable to display preview. Download preview PDF.
- Brown, B. W. Jr. (1959). Some properties of the Spearman estimator in bioassay,Tech. Report No. 6, Department of Statistics, University of Minnesota, Minneapolis, Minnesota.Google Scholar
- Finney,D. J. (1971).Probit Analysis, 3rd ed., Cambridge University Press.Google Scholar
- Spearman, C. (1908). The method of ‘right and wrong cases’ (‘constant stimuli’) without Gauss' formula,Brit. J. Psychol.,2, 227–242.Google Scholar
- Weaver, O. R. (1957). Using attributes for measurement of continuous variables in the rocket industry,Proc. 12th Midwest Quality Control Conference, American Society for Quality Control.Google Scholar