Efficiency of maximum likelihood estimation for a multinomial distribution with known probability sums
Statistics Theory
2021-06-07 v2 Statistics Theory
Abstract
For a multinomial distribution, suppose that we have prior knowledge of the sum of the probabilities of some categories. This allows us to construct a submodel in a full (i.e., no-restriction) model. Maximum likelihood estimation (MLE) under this submodel is expected to have better estimation efficiency than MLE under the full model. This article presents the asymptotic expansion of the risk of MLE with respect to Kullback--Leibler divergence for both the full model and submodel. The results reveal that, using the submodel, the reduction of the risk is quite small in some cases. Furthermore, when the sample size is small, the use of the subomodel can increase the risk.
Cite
@article{arxiv.1906.05461,
title = {Efficiency of maximum likelihood estimation for a multinomial distribution with known probability sums},
author = {Yo Sheena},
journal= {arXiv preprint arXiv:1906.05461},
year = {2021}
}