𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Estimation of Multinomial Probabilities under a Model Constraint

✍ Scribed by A.K. Gupta; A.K.Md. Ehsanes Saleh

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
396 KB
Volume
58
Category
Article
ISSN
0047-259X

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper estimation of the probabilities of a multinomial distribution has been studied. The five estimators considered are: unrestricted estimator (UE), restricted estimator (RE) (under model M), preliminary test estimator (PTE) based on a test of the model M, shrinkage estimator (SE) and the positive-rule shrinkage estimator (PRSE). Asymptotic distributions of these estimators are given under Pitman alternatives and the asymptotic risk under a quadratic loss has been evaluated. The relative performance of the five estimators is then studied with respect to their asymptotic distributional risks (ADR). It is seen that neither of the preliminary test and shrinkage estimators dominates the other, though each fares well relative to the other estimators. However, the positive rule estimator is recommended for use for dimension 3 or more while the PTE is recommended for dimension less than 3.

πŸ“œ SIMILAR VOLUMES

A computer program for maximum likelihoo
A computer program for maximum likelihood estimation of survival probabilities under a logistic model
✍ Sonja Johansen πŸ“‚ Article πŸ“… 1973 πŸ› Elsevier Science βš– 365 KB

Physical examinations made at annual or other fixed time intervals on each member of a group of healthy individuals yield sets of random variables measured over time, called time series. A computer program has been written which treats these measurements as predictor variables to be used in estimati