We consider a nonparametric model $\mathcal{E}^{n},$ generated by independent observations $X_{i},$ $i=1,...,n,$ with densities $p(x,\theta_{i}),$ $i=1,...,n,$ the parameters of which $\theta _{i}=f(i/n)\in \Theta $ are driven by the values of an unknown function $f:[0,1]\rightarrow \Theta $ in a smoothness class. The main result of the paper is that, under regularity assumptions, this model can be approximated, in the sense of the Le Cam deficiency pseudodistance, by a nonparametric Gaussian shift model $Y_{i}=\Gamma (f(i/n))+\varepsilon _{i},$ where $\varepsilon_{1},...,\varepsilon _{n}$ are i.i.d. standard normal r.v.'s, the function $\Gamma (\theta ):\Theta \rightarrow \mathrm{R}$ satisfies $\Gamma ^{\prime}(\theta )=\sqrt{I(\theta )}$ and $I(\theta )$ is the Fisher information corresponding to the density $p(x,\theta ).$

翻译：我们考虑一个非参数模型 $\mathcal{E}^{n},$ 该模型由独立观测 $X_{i},$ $i=1,...,n$ 生成，其密度函数为 $p(x,\theta_{i}),$ $i=1,...,n$。这些参数 $\theta _{i}=f(i/n)\in \Theta $ 由一个属于某个光滑性类别的未知函数 $f:[0,1]\rightarrow \Theta $ 的取值所驱动。本文的主要结果是，在正则性假设下，该模型可以在 Le Cam 亏欠伪距离的意义上，由一个非参数高斯平移模型 $Y_{i}=\Gamma (f(i/n))+\varepsilon _{i}$ 来近似，其中 $\varepsilon_{1},...,\varepsilon _{n}$ 是独立同分布的标准正态随机变量，函数 $\Gamma (\theta ):\Theta \rightarrow \mathrm{R}$ 满足 $\Gamma ^{\prime}(\theta )=\sqrt{I(\theta )}$，而 $I(\theta )$ 是对应于密度 $p(x,\theta )$ 的 Fisher 信息量。