问题 若 $x=(x_1, x_2, \cdots, x_n)$ 为从分布族 $f(x, \theta)=C(\theta) \exp \left\{\sum_{i=1}^k Q_i(\theta) T_i(x)\right\} h(x)$ 中抽取的简单样本, 试证 $T(x)=\left(\sum_{j=1}^n T_1\left(x_j\right), \sum_{j=1}^n T_2\left(x_j\right), \cdots, \sum_{j=1}^n T_k\left(x_j\right)\right)$ 为充分统计量. ## 答案 由于样本 $\mathbf{x} = (x_1, x_2, \dotsc, x_n)$ 是从分布族 $$ p(x;\theta) = C(\theta) \exp\left{ \sum_{i=1}^{k} Q_i(\theta) T_i(x)

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