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| GEOMETRIC METHOD OF SEQUENTIAL ESTIMATION RELATED TOMULTINOMIAL DISTRIBUTION MODELS |
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Citation： |
Wei Bocheng,Li Shouye.GEOMETRIC METHOD OF SEQUENTIAL ESTIMATION RELATED TOMULTINOMIAL DISTRIBUTION MODELS[J].Chinese Annals of Mathematics B,1995,16(4):489~500 |
| Page view： 1058
Net amount： 840 |
Authors： |
Wei Bocheng; Li Shouye |
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| Abstract： |
In 1980's, differential geometric methods are successfully used
to study curved exponential families and normal nonlinear
regression models. This paper presents a new geometric
structure to study multinomial distribution models which contain a
set of nonlinear parameters. Based on this geometric structure,
the authors study several asymptotic properties for sequential estimation.
The bias, the variance and the information loss of the sequential
estimates are given from geometric viewpoint, and a limit theorem
connected with the observed and expected Fisher information is
obtained in terms of curvature measures. The results show that the
sequential estimation procedure has some better properties which
are generally impossible for nonsequential estimation procedures. |
Keywords： |
Multinomial distribution model, Statistical curvature, Sequential estimation,Stopping rule, Fisher information, Information loss. |
Classification： |
62F |
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