Asymptotic Distribution of the Likelihood Function in the Independent not Identically Distributed Case
独立但不同分布情形下似然函数的渐近分布
Let $\Theta$ be an open subset of $R^k$ and for each $\theta \in \Theta$, let $X_1, \cdots, X_n$ be independent rv's defined on the probability space $(\mathscr{X}, \mathscr{A}, P_\theta)$, and let $p_{j, \theta}$ be the distribution of the rv $X_j$. Let $f_j(\bullet; \theta)$ be a specified version of the Radon-Nikodym derivative of $p_{j, \theta}$ with respect to a $\sigma$-finite measure $\mu$ and set $f_j(\theta) = f_j(X_j; \theta)$. Furthermore, for $\theta, \theta^\ast \in \Theta$…