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.

翻译：给定$n$个独立同分布观测，并依据Le Cam实验间缺陷概念度量获取附加观测的价值，我们证明对于某些类型的非参数实验，附加观测的价值以$1/\sqrt{n}$的速率递减。这与已知的参数实验中典型的$1/n$递减率以及超大规模实验中价值非减的情况不同。特别地，当观测来自仅知其密度被固定常数下界约束的样本时，该实验满足$1/\sqrt{n}$递减率。因此存在这样的实验：其附加观测的价值趋于零，但不存在任何一致估计量（依全变差距离）。