統計学輪講 第21回

It was shown that MLE is admissible on multinomial model with unrestricted parameter space, while MLE is inadmissible on multinomial model with restricted parameter space if the restricted parameter space satisfies some conditions, see Bruce (1971) and Funo (1991). However, they are both focused on squared error loss function.
In this talk, I would like to show the findings about estimation problem under quadratic loss function, which is a generalized case of squared error loss function. It is shown that MLE is still admissible on multinomial model with unrestricted parameter space. For estimation problem on multinomial model with restricted parameter space, we show that MLE is inadmissible if the restricted parameter space satisfies some conditions and parameter n is large enough.