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以给定一般指数族为共轭先验族的抽样模型AI 解读

Let $\mathscr{K} = \{K_\lambda: \lambda \in \Lambda\}$ be a family of sampling distributions for the data $x$ on a sample space $\mathscr{X}$ which is indexed by a parameter $\lambda \in \Lambda,$ and let $\mathscr{F}$ be a family of priors on $\Lambda$. Then $\mathscr{F}$ is said to be conjugate for $\mathscr{K}$ if it is closed under sampling, that is, if the posterior distributions of $\lambda$ given the data $x$ belong to $\mathscr{F}$ for almost all $x$. In this paper,…

线性指数族中的保符号无偏估计量AI 解读

Let ω G∈ Ω be a distribution parameter and r(ω) a positive estimand with range r(Ω). Hoeffding (1984) called an estimator that takes values only in r(Ω), including the boundaries of r(Ω), a range-preserving estimator. The range-preserving property is a sensible requirement to impose on an estimator. If we require unbiasedness, however, such estimators become difficult to find. In this article a less constraining condition, namely sign-preserving unbiasedness, is considered.…

某类指数模型中条件极大似然估计量的渐近行为AI 解读

SUMMARY In this paper we investigate the asymptotic behaviour of the conditional maximum likelihood estimator in an exponential model of order 2 introduced in Bar-Lev and Reiser (1982). This model, with natural parameters θ1 and θ2 (the latter a nuisance parameter), is characterized by expressing θ2 as a particular function of the mixed parameters. A direct proof is given for the asymptotic equivalence of the conditional maximum likelihood estimator and the maximum…