论文标题
在不可估计的非参数实验的其他观察结果中的信息
Information in additional observations of a non-parametric experiment that is not estimable
论文作者
论文摘要
给定$ n $独立和相同分布的观察结果，并根据Le Cam在实验之间的缺陷概念来衡量获得额外观察的价值，我们显示了某些类型的非参数实验的观测值，即以$ 1/\ sqrt {n} $ $ 1/\ sqrt {n} $的速度下降的价值下降。对于参数实验的$ 1/n $，这与已知的典型降低不同，在非常大的实验的情况下，这是不同的。特别是，$ 1/\ sqrt {n} $的速率适用于通过观察从密度观察样品的实验，我们只知道它仅从下面的某个固定常数从下面界定。因此，存在一个实验，其中其他观察值的值趋于零，但对于没有一致的估计值（在总变化距离）中。
Given $n$ independent and identically distributed observations and measuring the value of obtaining an additional observation in terms of Le Cam's notion of deficiency between experiments, we show for certain types of non-parametric experiments that the value of an additional observation decreases at a rate of $1/\sqrt{n}$. This is distinct from the known typical decrease at a rate of $1/n$ for parametric experiments and the non-decreasing value in the case of very large experiments. In particular, the rate of $1/\sqrt{n}$ holds for the experiment given by observing samples from a density about which we know only that it is bounded from below by some fixed constant. Thus there exists an experiment where the value of additional observations tends to zero but for which no estimator that is consistent (in total variation distance) exists.
