We investigate adaptive density estimation in the additive model $Z=X+Y$, where $X$ and $Y$ are independent $d$-dimensional random vectors with non-negative coordinates. Our goal is to recover the density of $X$ from independent observations of $Z$, assuming the density of $Y$ is known. In the $d=1$ case, an estimation procedure using projection on the Laguerre basis has already been studied. We generalize this procedure in the multivariate case: we establish non-asymptotic upper bounds on the mean integrated squared error of the estimator and we derive convergence rates on anisotropic functional spaces. Moreover, we provide data-driven strategies for selecting the right projection space (for $d=1$, we improve the previous projection procedure). We illustrate these procedures on simulated data, and in dimension $d=1$ we compare our procedure with the previous adaptive projection procedure.

我们研究加性模型中的自适应密度估计 $ž=X+ÿ$， 在哪里 $X$ 和 $ÿ$ 是独立的 $d$非负坐标的三维随机向量。我们的目标是恢复$X$ 来自对 $ž$假设密度为 $ÿ$是众所周知的。在里面$d=\mathrm{1个}$在这种情况下，已经研究了使用基于Laguerre投影的估计程序。我们在多变量情况下推广此过程：我们在估计量的平均积分平方误差上建立非渐近上限，并得出各向异性函数空间上的收敛速度。此外，我们提供了数据驱动的策略来选择合适的投影空间（用于$d=\mathrm{1个}$，我们改进了之前的投影过程）。我们将在模拟数据和维度上说明这些程序$d=\mathrm{1个}$ 我们将我们的程序与先前的自适应投影程序进行了比较。