Simultaneous Estimation in Discrete Multivariate Exponential Families
离散多元指数族中的同时估计
Let $X$ have a discrete density of the form $f(x) = t(x)\xi(\theta)\theta^{x_1}_1 \cdots \theta^{x_p}_p$, where $t(x)$ is nonzero on some infinite subset of $Z^p$. Consider simultaneous estimation of the $\theta_i$ under the loss $\mathscr{L}_m(\theta, \delta) = \sum^p_{i = 1} \theta^{-m}_i(\theta_i - \delta_i)^2, m \geq 0$. For integers $m \geq 1$, estimators are found which improve on the maximum likelihood estimator or uniformly minimum variance unbiased estimator. The…